Seminario de Geometría

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Universidad de Granada
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Conferencias

The half-space property and entire positive minimal graphs in $M \times \mathbb{R}$

University College London

We show that a properly immersed minimal hypersurface in $M \times \mathbb{R}^+$ equals some $M \times \{c\}$ when $M$ is a complete, recurrent n-dimensional Riemannian manifold with bounded curvature. If on the other hand, $M$ has nonnegative Ricci curvature with curvature bounded below, the same result holds for any positive entire minimal graph over $M$.
This is joint work with H. Rosenberg and J. Spruck.

Seminario Matemáticas. 1ª planta

Double and triple bubbles

Brigham Young University

We present a new proof of the double bubble conjecture in $\mathbb{R}^n$ and we discuss an strategy to prove the triple bubble conjecture in $\mathbb R^3$.

Seminario de Matemáticas. 1ª planta

Homotopy of area decreasing maps by mean curvature flow

Leibniz Universität Hannover

Let $f:M\to N$ be a smooth area decreasing map between Riemannian manifolds $(M,g_m)$ and $(N,g_n)$. Under weak and natural assumptions on the curvatures of $(M,g_m)$ and $(N, g_n)$, we prove that the mean curvature flow provides a smooth homotopy of $f$ into a constant map.

Seminario Matemáticas. 1ª planta

Multiplicity results for $p$-Laplacian problems

Politecnico di Bari

The aim of this talk is to present some recent results about the existence and the multiplicity of solutions of the elliptic problem $$(P)\qquad\qquad \left\{ \begin{array}{lll} \displaystyle{-\Delta_p u\ =\ g(x, u) + \varepsilon h(x, u)} & \mbox{ in } \Omega,\\ \displaystyle{u=0} & \mbox{ on } \partial\Omega,\\ \end{array} \right. $$ where $1\lt p\lt +\infty$, $\Delta_p u= {\rm div}(|\nabla u|^{p-2}\nabla u)$, $\Omega$ is an open bounded domain of ${\bf R}^N$ with smooth boundary $\partial\Omega$, $\varepsilon\in {\bf R}$, $g$ is subcritical and asymptotically $(p-1)$-linear at infinity and $h$ is just a continuous function. For $p=2$, even when this problem has not a variational structure on $W^{1,2}_0(\Omega)$, suitable procedures and estimates allow us to prove that the number of distinct critical levels of the functional associated to the unperturbed problem is "stable" under small perturbations, in particular obtaining multiplicity results if $g$ is odd, both in the non-resonant and in the resonant case. For $p\not=2$ and $\varepsilon=0$, we get the existence and the multiplicity of solutions of the quasilinear elliptic problem $(P)$ by means of some abstract critical point theorems on Banach spaces and using two sequences of quasi-eigenvalues for the $p$-Laplacian operator. Finally we use the so-called Bolle's method to get the existence of infinitely many solutions of $(P)$ when $g(x,u)=|u|^{q-2}$, $p \lt q \lt p^\ast$, $\varepsilon=1$, $h(x,u)=h(x)$ and $u=\varphi$ on $\partial\Omega$, with $\varphi\in C^2(\overline\Omega)$.

Seminario de Matemáticas. 1ª planta

Cubic minimal cones and Jordan algebras

Linköping University

A classification and construction of algebraic minimal cones of degree higher or equal than 3 remains a long-standing difficult problem. We will discuss the first non-trivial case of cubic minimal cones, and, radial eigencubics in particular (the study initiated earlier by Hsiang in [Hsia67]). We show that there are hidden Clifford and Jordan algebra structures associated with the radial eigencubics, and specify the latter in the context of the eiconal type equation $\|Du(x)\|^2=9\|x\|^4$ which plays a crucial role in the classification [Tk10]. In particular, we establish a natural bijective correspondence between cubic solutions of the eiconal type equation with a general (not necessarily Euclidean) norm $\|\cdot\|$ and semi-simple rang three Jordan algebras. We also illustrate the appearance of cubic Jordan algebras by some related problems discussed recently in [NTV12].
[Hsia67] Wu-yi Hsiang, Remarks on closed minimal submanifolds in the standard Riemannian m-sphere, J. Differential Geometry 1 (1967), 257–267.
[NTV12] N. Nadirashvili, V.G. Tkachev, and S. Vladut, A non-classical solution to a Hessian equation from Cartan isoparametric cubic, Adv. Math. 231 (2012), no. 3-4, 1589–1597.
[Tk10] V. G. Tkachev, A generalization of Cartan's theorem on isoparametric cubics, Proc. Amer. Math. Soc. 138 (2010), no. 8, 2889–2895.

Seminario Matemáticas. 1ª planta

Superficies mínimas con crecimiento de curvatura cuadrático

Universidad de Granada

Para una superficie en $\mathbb{R}^3$, la función $f=K R^2$ (curvatura de Gauss por distancia al cuadrado extrínseca) es invariante por reescala. Veremos dos resultados sobre cómo esta función controla distintos aspectos de la teoría de superficies mínimas embebidas:
1) Cuándo una singularidad aislada en una superficie mínima es evitable.
2) Caracterización de las superficies completas con curvatura total finita como aquellas que tienen f acotada.
Las herramientas principales para demostrar estos resultados serán la fórmula de monotonía para superficies mínimas y una generalización de la clasificación de superficies completas mínimas estables en $\mathbb{R}^3$ al caso en que sólo se exige completitud fuera de un punto.

Seminario Matemáticas. 1ª planta

Some new result on sub-Riemannian geodesics in Carnot groups

Università degli Studi di Padova

We present some result on sub-Riemannian geodesics in Carnot groups recently obtained in collaboration with E. Le Donne, G.P. Leonardi, and R. Monti. A sub-Riemannian manifold is a manifold M endowed with a distinguished subbundle D of the tangent bundle and with a metric on D. A distance (called sub-Riemannian) on M can be defined on minimizing the length among curves which are tangent to D. One of the main open problems in the field is the regularity of length minimizers, that is not trivial due to the presence of the so called abnormal curves. We provide a characterization of abnormal geodesic in Carnot groups (i.e., certain Lie groups which are the infinitesimal models of sub-Riemannian manifolds) showing that they are contained in certain algebraic varieties; this poses several questions ranging from analysis to algebraic geometry. Applications to the problem of geodesics' regularity will be discussed.

Seminario Matemáticas. 1ª planta

Gluing constructions for complete minimal surfaces with finite total curvature in $\mathbb{H}^2 \times \mathbb{R}$

Universidad de Granada

We construct the first examples of complete, properly embedded minimal surfaces in $\mathbb{H}^2 \times \mathbb{R}$ with finite total curvature and positive genus. These are constructed by gluing copies of the horizontal catenoid.
This is a joint work with Rafe Mazzeo and Magdalena Rodríguez.

Seminario Matemáticas. 1ª planta

The Yang-Mills gradient flow and its variants

Max-Planck-Institut für Mathematik

We review our construction of a Morse homology theory for the Yang-Mills gradient flow in two dimensions and its relation to Weber's heat flow homology. We discuss compactness and Morse-Smale transversality for the perturbed flow, which invokes a novel $L^2$ local slice theorem due to Mrowka-Wehrheim. Finally we show how a modified Yang-Mills functional leads to an "elliptic Yang-Mills flow" for which a Floer type homology theory is currently under construction. (Last part in joint work with R. Janner).

Seminario de Matemáticas (1ª Planta, Sección de Matemáticas)

Graphs with prescribed curvature in warped products

Universidad de Ceará

We discuss existence results for graphs with prescribed r-mean curvature in Riemannian manifolds endowed with either a Killing or a conformal vector field

Seminario de Matemáticas (1ª Planta, Sección de Matemáticas)

Bäcklund Type Transformations and Superposition Formulae for a Class of Differential Equations

Universidade de Brasilia

We consider the partial differential equations whose solutions characterize the linear Weingarten surfaces in space forms. This is a class of seven equations that includes the elliptic sinh-Gordon, the elliptic cosh-Gordon, the sine-Gordon, the Liouville and the Laplace equations. Given a solution of such a differential equation, we will show that the geometric Ribaucour transformation for linear Weingarten surfaces generates a Bäcklund type transformation, which is an integrable system that provides families of new solutions of the same differential equation. The permutability property provides superposition formulae which give new solutions algebraically. Explicit examples will be included.
Conferencia dentro del programa de doctorado Matemáticas

Seminario de Matemáticas. 1ª Planta. Sección de Matemáticas

Floating bodies in equilibrium

Stanford University

Written literature on this topic can be traced at least to Aristoteles about 350 BC, and relevant questions are addressed sporadically in classical literature; however few reliable quantitative predictions are available. Currently open problems are becoming recognized (among them a curious connection with billiards theory), and there is activity toward resolving them. I will discuss the current state of that theory, with emphasis on the question of determining when a body whose density exceeds that of a given liquid can be made to float on a surface of that liquid. Much of the new material I will cover is joint with T.I. Vogel.

Seminario de Matemáticas. 2ª Planta, sección de Matemáticas.

Stable submanifolds with constant mean curvature: A variational approach to the isoperimetric problem in higher codimension

Centre for Physics of Fundamental Interactions, Lisboa, Portugal

In [Mo], [Sa], [Mo-Sa], variational characterizations of $m$-dimensional submanifolds with prescribed (possibly constant) mean curvature are described in higher codimension by introducing several notions of "enclosed volume", generalizing the well known classical case of codimension one, due to Barbosa, do Carmo and Eschenburg. In these settings, these submanifolds are critical points for the area functional under the enclosed volume constraint and we discuss when minimizers exist, that is, they solve an isoperimetric problem, and their uniqueness. When the ambient space is endowed by a rank $m+1$ calibration, with consequent definition of enclosed volume, we use the second variation of the area and volume functionals to define stability. Then we ask if spheres uniquely solve the isoperimetric problem and if are stable ([Sa1][Mo-Sa][Sa2]).

References:

  • [Mo] Frank Morgan, "Perimeter-minimizing curves and surfaces in $\mathbb{R}^n$ enclosing prescribed multi-volume", Asian J. Math. 4 (2000), 373-382.
  • [Sa1] I.Salavessa, "Stability of submanifolds with parallel mean curvature in calibrated manifolds", Bull. Braz. Math. Soc. 41 (2010), 495-530.
  • [Mo-Sa], F. Morgan and I.Salavessa. "The ispoperimetric problem in higher codimension".
  • [Sa2] I.Salavessa. "Stable 3-spheres in C3", J. Mathematics Research 4 , no.2 (April) 2012

Seminario de Matemáticas. 1ª Planta. Sección de Matemáticas

Surfaces making constant angle with certain vector fields in 3-spaces

Katholieke Universiteit Leuven

A surface is called a constant angle surface if its unit normal makes a constant angle with a "fixed" direction. Starting from this general definition, we give different choices of directions in order to study and classify constant angle surfaces. Firstly, in the Euclidean 3-space, one of the coordinates axes, the position vector field, or a Killing vector field may be chosen as a "fixed" direction. Secondly, recent classification results for constant angle surfaces in solvable Lie groups are obtained.

Seminario de Matemáticas. 1ª Planta. Sección de Matemáticas

Almost complex curves (=surfaces) of the nearly Kaehler $S^3 \times S^3$

Université de Valenciennes

In recent years due to the work of amongst others Butruille, Spiro, Podesta and Nagy a considerable amount of progress has been made in the study and classification of nearly Kaehler maniolfds. According to Nagy’s structure theorem any complete strict nearly kaeher manifol is finitely covered by a product of homogeneous 3-symmetric manifolds, twistor spaces of positive quaternion Kaehler manifolds with their canonical NK structur and six dimensional strict NK manifolds. This is one of the reasons which raise a particular interest for six dimensional strict NK structures. It is also known that, in six dimensions, the “strictness” condition is equivalent to the fact that the NK structure is not Kaehler and that strict NK manifolds are automatically Einstein and related with the existence of a nonzero Killing spinor.Other reasons of interest for NK structures in six dimensions are provided by their relations with geometries with torsion, G2-holonomy and supersymmetric models. The only homogeneous strict NK manifolds in six dimensions are the six dimensional 3-symmetric spaces endowed with their natural NK structures, namely the standard sphere $S^6 = G2/SU3$, the twistor spaces $ CP2 = Sp2/U(1) \times Sp1$ and $F = SU3/U(1)^2$ and the space $S^3 \times S^3$. Whereas submanifolds of $S^6$ are well understood by now, this is not yet the case for submanifolds of $S^3\times S^3$ (with respect to this nearly Kaehler structure). Not that the metric associated with this structure is not the standard metric on $S^3 \times S^3$. The aim of this lecture is to present the structure in an elementary way which will allow the systematic study of its submanifolds. We will then focus on almost complex curves for which we will introduce a holomorphic differential. Further results include a classification of all totally geodesic almost complex curves as well as as the result that an almost complex $S^2$ is totally geodesic.

Seminario de Matemáticas. 1ª Planta. Sección de Matemáticas

Variations on Two Themes by Hermann Amandus Schwarz

Indiana University

This talk will consist of three parts:
First, I will explain how the Schwarz-Christoffel formula for holomorphic maps to Euclidean polygons can be used to elegantly construct minimal surfaces.
Secondly, I will show a variant of this formula that works for periodic Euclidean polygons and use it to construct examples of triply periodic minimal surfaces.
Finally, as an application, I will show a deformation of the H-surface of Schwarz into the P-surface. Time permitting, there will be a fourth part showing rather surprising deformations of some triply periodic genus 4 surfaces that are also based on the periodic Schwarz-Christoffel formula.
Conferencia dentro del complemento de formación del Doctorado interuniversitario Matemáticas

Seminario de Matemáticas. 1ª Planta. Sección de Matemáticas

Spectral positivity on surfaces

Université Montpellier II

We consider operators of the form $\Delta+aK$ on a Riemannian surface. Such operators naturally appear when considering the stability operator of a minimal surface in a 3-manifold. In particular, when studying the stability of minimal surfaces, a natural problem is to derive geometric properties of the surface from the positivity of the operator. In this talk we will prove that the positivity of $\Delta+aK$ on a Riemannian surface (with additional hypotheses when $a\le\frac{1}{4}$) imply that the surface is conformally equivalent to $\mathbb{C}$ or $ \mathbb{C}^*$, and in the second case we will prove that the metric is flat. We shall see that our statements are sharp, improving former results on the subject. This is a joint work with Pierre Bérard.

Seminario Matemáticas. 1ª planta. Sección de Matemáticas

Superficies totalmente umbilicales en grupos de Lie métricos tridimensionales

Universidad de Jaén

En esta charla, analizaremos y clasificaremos las superficies totalmente umbilicales en los grupos de Lie métricos tridimensionales, tanto en el caso unimodular como en el no-unimodular.
Este es un trabajo conjunto con Rabah Souam.

Seminario de Matemáticas. 1ª Planta. Sección de Matemáticas

Bernstein problems in higher codimension

Korea Institute for Advanced Study

Para más información véase el archivo adjunto a la conferencia.

Seminario Matemáticas. 1ª planta

La Geometría de un problema elíptico sobredeterminado

Universidad de Granada

Dado un dominio plano y una funcion $f$, consideramos la ecuación $\Delta u + f(u) =0$, $u>0$ en $\Omega$ con condiciones de Dirichlet y Neumann en la frontera, simultáneamente, $u=0$, $u_\nu=c$ en $\partial\Omega$. Si el dominio es acotado, Serrin demuestra que $\Omega$ es un disco y $u$ es radial. Para dominios no acotados hay muchas cuestiones abiertas y presentamos algunos resultados obtenidos con Pieralberto Sicbaldi y relacionados con la teoría de superficies de curvatura media constante: dominios con topología finita, teorema del semiplano, etc.

Seminario Matemáticas. 1ª planta

The Willmore and other $L^2$ curvature functionals in Riemannian manifolds

Scuola Normale Superiore (Pisa)

Given an immersion of a surface into the euclidean 3 space, the Willmore functional is defined as the $ L^2$ norm of the mean curvature. If we consider immersions in a Riemannian manifold there are many possible generalizations of the Willmore functional; in the seminar we will speak about these generalizations and study the existence of minimizers and critical points of the corresponding functionals under curvature conditions on the ambient manifold. The topic has links with general relativity, string theory, biology, nonlinear elasticity theory etc.

Seminario Matemáticas. 1ª planta

Sobre experimentos realizados en el Max Planck Institute (MIPKG): bifurcando cilindros

Universidad de Granada

Experimentos realizados en el campo de microfluidos en el MIPKG de Potsdam, muestran que ciertos fluidos confinados en bandas hidrófilas cambian bruscamente de forma al ir depositando más líquido. Las configuraciones iniciales son cilindros, pero después de cierto estadio, aparecen bultos y protuberancias: ver Gau et al. Science 283 (1999), 46. Realizamos una demostración matemática de tales fenómenos basada en la teoría de bifurcación por autovalores simples de Crandall-Rabinowitz.

Seminario Matemáticas. 1ª planta

Area preserving transformations in 2 dimensional space forms and classical differential geometry

Universidade de Brasília

We will show how to construct area preserving transformations (APT) between domains in two dimensional space forms starting with a differentiable function. As an application, we show how this method of construction of APT reveals the connections between APT and some special Laguerre minimal surfaces.
This is joint work with W.P.Ferreira.

Seminario Matemáticas. 1ª planta

Recent results on Homogeneous Hypersurfaces in Hermitian Symmetric Spaces of rank 2

Kyungpook National University

Seminario de Matemáticas. 1ª Planta. Sección de Matemáticas

Maximum Principles and their Applications to Real and Complex submanifolds

Kyungpook National University

Seminario de Análisis Matemático. 1ª Planta, sección de Matemáticas

Difeomorfismos armónicos entre dominios de la esfera

Universidad de Granada

Discutiremos sobre la existencia o no de difeomorfismos armónicos entre diferentes dominios de la esfera euclídea de dimensión 2. Trabajo en colaboración con Rabah Souam.
arXiv:1108.1960v2 [math.DG]

Seminario de Matemáticas. 1ª Planta. Sección de Matemáticas

Hipersuperficies conformemente llanas en $\mathbb{R}^4$ y superficies llanas del espacio hiperbólico asociadas

Universidade de Brasilia

Presentaremos un estudio de hipersuperficies conformemente llanas en $\mathbb{R}^4$ relacionadas con soluciones de un sistema de equaciones diferenciales parciales invariantes por un grupo de simetría. Asociadas a una clase particular de las soluciones del sistema, obtenemos una clase de superficies llanas en el espacio hiperbólico que son invariantes por un movimiento helicoidal, así que presentaremos también una clasificación de estas superficies en términos de datos holomorfos y una caracterización a través de las primera y segunda forma fundamentales.

Seminario de Matemáticas. 1ª Planta, sección de Matemáticas.

Hipersuperficies con una dirección principal canónica

Instituto de Matemáticas, Universidad Nacional Autónoma de México

Dado un campo vectorial $X$ en una variedad Riemanniana, decimos que una hipersuperficie tiene dirección principal canónica relativa a $X$, si la proyección ortogonal de $X$ sobre el espacio tangente de $M$ da una dirección principal de $M$. Daremos varias caracterizaciones de estas hipersuperficies. En particular se relacionan con funciones transnormales y funciones eikonales. Como aplicación, obtendremos una caracterización de las superficies de Delaunay como las únicas superficies en $\mathbb{R}^3$ con curvatura media constante que admiten una dirección principal canónica.

Seminario de Matemáticas. 1ª Planta, sección de Matemáticas.

Eventos

Workshop on Geometric Structures in PDE

ICMAT, Madrid (Spain)

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Invited speakers

  • Robert Kusner (U. Massachusetts): The space of soap bubbles
  • Pablo Angulo (UAM): Inverse Calderon problem on a Riemannian manifold and limiting Carleman weights
  • Fabricio Maciá (UPM): Schrödinger flows and curvature
  • Jason Cantarella (U. Georgia): Quaternionic Geometry of Closed Polygons and Curves

Organizers

Alberto Enciso and Daniel Peralta-Salas

Workshop Geometric and Complex Analysis

Granada (Spain)

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The Department of Geometry and Topology of the University of Granada will host a two-day conference on November 22-23, 2012.
The aim of the workshop is to bring together people working in Geometric Analysis. The meeting consists of two different sessions; one of them covering the most geometric aspects of submanifold theory and the other one covering the most complex analytic ones.
There will be ample opportunities for discussions and interactions among the participants.

Organizing committee

  • Antonio Alarcón (alarcon(at)ugr.es)
  • Franc Forstneric
  • Francisco J. lópez (fjlopez(at)ugr.es)

Conferenciantes invitados

Seminar on Mathematical General Relativity

Paris (France)

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Invited speakers

  • Miguel Sánchez Caja (Granada): Recent interrelated progress in Lorentzian, Finslerian and Riemannian Geometry
  • Mike Scherfner (Berlin): CTC’s and time machine structure: Some history and new developments
  • Vladimir Matveev (Jena): Geodesic degree of mobility of lorentzian metrics
  • Philippe G. LeFloch (Paris): Injectivity radius and canonical foliations of Einstein spacetimes
  • Mehdi Belraouti (Avignon): Asymptotic behavior of level sets of a convex time function
  • Ghani Zeghib (Lyon) Actions on the circle and isometry groups of globally hyperbolic Lorentz surfaces
  • Eduardo Garcia-Rio (Santiago de Compostela): Quasi-Einstein and Ricci soliton Lorentzian metrics

Lectures on stable minimal surfaces

Granada (España)

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In the first part of these lectures, the aim is the topological and geometric classification of complete stable $H-$surfaces immersed in a manifold $(\amb , g)$ whose Scalar curvature is nonnegative. Here, we will show the H. Rosenberg's diameter estimate [Rosen06] (following ideas of D. Fischer-Colbrie [Fis85]) and the classification of complete stable minimal surfaces given by D. Fischer- Colbrie and R. Schoen [FS80] and R. Schoen and S.T. Yau [SY82]. We take the point of view of stable Schrodinger operators as in the work of Meeks-Pérez-Ros [MPR08].

In the second part, we classify manifolds $(\amb , g)$ under the existence of certain compact area minimizing surface and a lower bound of its Scalar curvature. We will show area estimates for stable compact minimal surfaces and in the case that estimated is attained, we will show how the manifold splits locally around such an area minimizing surface. In the case we also add conditions saying that such a surface is area minimizing on its homotopy class and attains the estimate, the splitting is global. The idea is to extend the splitting theorems developed by Cai-Galloway [CG00], Bray-Brendle-Neves [BBN10], I. Nunes [Nun12]. Here, we will take the unified point of view considered by Micallef-Moraru [MM].

Conferencia financiado por el programa de doctorado Matemáticas (MHE2011-00248).

References

[BBN10]
H. Bray, S. Brendle, A. Neves, Rigidity of area-minimizing two-spheres in three-manifolds, Comm. Anal. Geom., 18 (2010), 821-830.
[CG00]
M. Cai and G. Galloway, Rigidity of area minimizing tori in 3-manifolds of nonnegative scalar curvature, Comm. Anal. Geom., 8 (2000), 565-573.
[Esp10]
J. M. Espinar, Rigidity of stable cylinders in three-manifolds. To appear in Proc. A.M.S.
[Fis85]
D. Fischer-Colbrie, On complete minimal surfaces with finite Morse index in three manifolds, Invent. Math., 82 (1985), 121-132.
[FS80]
D. Fischer-Colbrie, R. Schoen, The structure of complete stable minimal surfaces in 3-manifolds of nonnegative scalar curvature, Comm. Pure and Appl. Math., 33 (1980), 199-211.
[MPR08]
W. Meeks, J. Pérez and A. Ros, Stable constant mean curvature hypersurfaces, Handbook of Geometric Analisys, volume 1 (2008), pages 381-380. International Press, edited by Lizhen Ji, Peter Li, Richard Schoen and Leon Simon, ISBN: 978-1-57146-130-8.
[MM]
M. Micallef, V. Moraru, Splitting of three-manifolds and rigidity of area-minimizing surfaces. Preprint.
[Nun12]
I. Nunes, Rigidity of Area-Minimizing hyperbolic surfaces in three-manifolds. To appear in J. Geom. Anal.
[Rosen06]
H.Rosenberg, Constant mean curvature surfaces in homogeneously regular 3-manifolds, Bull. Austral. Math. Soc.,74 (2006), 227-238.
[SY82]
R. Schoen, S.T. Yau, Complete three dimensional manifolds with positive Ricci curvature and scalar curvature, Ann. Math. Stud., 102 (1982), 209-228.

Conferenciantes invitados

Superficies propiamente embebidas de curvatura media constante en $\mathbb{R}^3$

Granada (España)

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En este curso se presenta una introducción a la teoría clásica de Korevaar-Kusner-Solomon-Meeks sobre superficies de curvatura media constante (distinta de cero) propiamente embebidas en $R^3$ con topología finita. La finalidad es probar los siguientes tres resultados: sea S una superficie en las condiciones anteriores. Entonces:

  • Todos los finales de S están cilíndricamente acotados.
  • S no puede tener un solo final.
  • Si S tiene dos finales, entonces es una superficie de revolución.

Asimismo, explicaremos cómo el teorema anterior funciona para clases de superficies mucho más generales, como superficies especiales de Weingarten de un cierto tipo (teorema de Espinar-Gálvez-Rosenberg).

Finalmente, y si el tiempo lo permite, analizaremos la extensión de este tipo de ideas al caso de superficies de curvatura media constante en ciertos espacios homogéneos tridimensionales.

Conferencia financiada por el programa de doctorado Matemáticas (MHE2011-00248)

Conferenciantes invitados

Workshop of Young Researchers in Mathematics

Madrid (Spain)

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Conformal and Kähler Geometry

Institut Henri Poincaré (Paris, France)

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Mini-courses

  • Olivier Druet (ENS-Lyon): An introduction to conformal geometry.
  • Simon Brendle (Stanford University): The Sphere Theorem.
  • Fernando Marquez (IMPA): The Yamabe problem: compactness and noncompactness questions.
  • Olivier Biquard (UPMC): Asymptotic geometry of Einstein metrics.
  • Claude LeBrun (Stony Brook): Curvature functionals, Kähler metrics, and the geometry of 4-manifolds.
  • Sean Paul (University of Wisconsin): An introduction to the Tian-Yau-Donalsdon conjecture.
  • Piotr Chruściel (University of Vienna): Introduction to the Cauchy problem in general relativity.

Conferences

  • September 17 – 21: Conformal and Kähler Geometry - IHP.
  • October 08 – 12: Journées de Physique Mathématiques - IHP.
  • October 22 – 26: Recent Developments in Conformal Geometry - Université de Nantes.
  • November 05 – 09: Geometric PDEs - IHP.
  • December 10 – 14: Recent Developments in Kähler Geometry - IHP.

Workshop Geometric Flows and Geometric Structures

Valencia (Spain)

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The aim of this workshop is to bring together experts in the fields of geometric flows and geometric structures. Morning sessions will be devoted to lectures given by invited speakers. Workgroups and informal talks on topics of interest suggested by the participants will be held in the afternoons.

Geometry of minimal surfaces via integrable systems

Granada (Spain)

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Professor Laurent Hauswirth will give a four-day course entitled Geometry of minimal surfaces via integrable systems.
In this lecture, he will explain how we can construct and solve the period problem for minimal annuli in $\mathbb{S}^2\times\mathbb{R}$ and $\mathbb{S}^3$. Then we will explain how we can deform this annuli preserving the period and embeddness via Whitham deformation. We prove that the space moduli of embedded minimal annuli is path connected. Isolated property of annuli foliated by circles imply uniqueness of classical embedded examples. This theory apply to find a proof of Lawson conjecture and and present an unified theory with the classification of genus zero embedded minimal surfaces of $\mathbb{R}^3$ and $\mathbb{S}^2\times\mathbb{R}$.

Conferencia financiada por el programa de doctorado Matemáticas (MHE2011-00248)

Conferenciantes invitados

Indo-Spanish Conference on Geometry and Analysis

Madrid (Spain).

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The main goal of this meeting is to foster interaction and collaboration between Indian, Spanish and other European mathematicians in the areas of algebraic geometry and harmonic analysis. The meeting is part of a more general project for Indo-Spanish collaboration in Mathematics.

Spanish Relativity Meeting in Portugal

Guimaraes, Portugal

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The Spanish Relativity Meeting (ERE) is an international conference devoted to Relativity and Gravitation which is organized every year by one of the Spanish or Portuguese groups working in this area. It is supported by the Spanish Society of Gravitation and Relativity (SEGRE).

Symmetries in Differential Geometry and Mathematical Physics

University of Luxembourg (Luxemburgo)

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The purpose of the conference is to bring together mathematicians and mathematical physicists working in related areas of Differential Geometry and Theoretical Physics. It is intended to present new results about the Geometry of symmetric and homogeneous spaces, Theory of Lie algebras and superalgebras, Lorentzian and pseudo-Riemannian Geometry, Spin Geometry, mathematical aspects of Supersymmetry. The conference is in honor of Prof. Dmitri Alekseevsky. The scientific committee is composed of: Jose Figueroa-O'Farrill (Edinburgh) Ivan Kolar (Brno) Martin Olbrich (Luxembourg) Martin Schlichenmaier (Luxembourg) Ernest B. Vinberg (Moscow) The following speakers have confirmed their presence Dmitri Alekseevsky (Brno) Helga Baum (HU Berlin) Said Benayadi (Metz) Jurgen Berndt (King's College London) Vicente Cortes (Hamburg) Liana David (IMAR Bucarest) Chandrashekar Devchand (Potsdam) Anton Galaev (Brno) Stefan Ivanov (Sofia) Victor Kac (MIT) Ines Kath (Greifswald) Stefano Marchiafava (Roma Sapienza) Andrea Spiro (Camerino) Andrew Swann (Aarhus) Gudlaugur Thorbergsson (Cologne) Please note that there is the possibility to submit short talk proposals.

Third Iberoamerican Meeting on Geometry, Mechanics and Control

Salamanca (Spain)

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The Iberoamerican Meetings on Geometry, Mechanics and Control are the result of the efforts of different research groups, in various Iberoamerican countries with interest in differential geometry, mechanics and control theory to establish scientific meetings of the specialty. These subject matters are highly topical, interacting in a common area of Mathematics, Physics, Mechanics, and Engineering.

This will be the third edition of a congress that came up with the idea of promoting the interactions between these disciplines, between the mathematical communities in these countries, while maintaining an international character. This type of conferences are important to keep and to strengthen contacts between the Spanish, Portuguese and Latin American groups and also establish a framework for spreading and for expand cooperation with researchers from other European countries, United States, Canada and China, among others.

One of the most important features of this series of conferences is the emphasis on the assistance and active participation of young researchers, with a dual purpose: contribute to improve their training by putting them in contact with great value senior researchers, and promote contact between themselves which could turn out in subsequent scientific collaborations.

Conference on Pure and Applied Differential Geometry

Leuven (Belgium)

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Topics: Minimal submanifolds, Lagrangian submanifolds and related topics, Affine differential geometry, Lorentzian geometry.
Invited Lecturers:
  • Ildefonso Castro (Universidad de Jaen)
  • Bang-Yen Chen (Michigan State University)
  • Benoît Daniel (Université Nancy 1) (tbc)
  • An-Min Li (Sichuan University)
  • Jason Lotay (UCL, London)
  • Vladimir Matveev (Universität Jena)
  • Udo Simon (T.U. Berlin)
  • Rabah Souam (Université Paris 7)

Workshop on Geometry of Interfaces and Capillarity

Granada (Spain)

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The objective of the workshop is to bring together researchers from mathematics and physics working on geometric problems involving interfaces, capillarity, surfaces with constant mean curvature and wetting phenomena.
Local Organizing Committee: Rafael López, Francisco Martín

Conferenciantes invitados

Geometric variational problems

Granada (Spain)

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Dentro del programa FisyMat Advanced Courses del programa de doctorado FisyMat, del 18 al 20 de junio de 2012 se impartirá el curso Geometric Variational Problems, coordinado por Manuel Ritoré.

El curso se desarrollará en la Sala de conferencias (sección de Matemáticas, planta baja) de 16:30 a 19:30 los días 18, 19 y 20 de junio.

Conferenciantes invitados

ICTP-ESF School and Conference on Geometric Analysis

Trieste (Italy)

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The Abdus Salam International Centre for Theoretical Physics (ICTP) is organizing a School and Conference on Geometric Analysis within the framework of the ICTP-ESF Series of High Level Conferences on Geometry and Dynamics. The activity will be held from 11 to 29 June 2012, in Trieste, Italy. It will be directed by C. Arezzo (ICTP, Trieste, Italy), F. Pacard (Ecole Polytechnique, Palaiseau, France) and R. Schoen (Stanford University, USA).

Main topics

  • Evolution equations on real and complex manifolds
  • Riemannian Geometry and General Relativity
  • Extremal Kähler metrics

The first two weeks (11 - 22 June) will be an Advanced School: six mini-courses of high level on the main topics above. There will be seminars and training activities for the participants. Some leading and famous mathematicians will present the mini-courses.

Invited Lecturers: S. Brendle (Stanford), F. Pacard (Ecole Polytechnique), T. Riviere (ETH), R. Schoen (Stanford), G. Tian (Princeton and Beijing), P. Topping (Warwick).

The third week (25 - 29 June) will be an International Conference on Geometric Analysis. Its primary aim is to promote interaction among the leaders in Geometric Analysis and to introduce and discuss front-line research with young participants from all over the world.

The tentative list of speakers of the third week's Conference (24-29 June), includes: R. Berman, Jingyi Chen, J. Corvino, J. Fine, V. Guedj, J. Isenberg, G. La Nave, C. Le Brun, Y.-I. Lee, Chi Li, Jiayu Li, A. Malchiodi, F. Marques, Song Sun, V. Tosatti, J. Viaclovsky, B. Wilking*, Xiaohua Zhu.
* to be confirmed

Participation

Mathematicians from all countries which are members of the United Nations, UNESCO or IAEA may attend the activity.

G 2 days

London (United Kingdom)

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The aim of the workshop is to bring together researchers working in G2 geometry as well as in other related areas. The meeting will also include introductory talks for researchers interested in learning about this exciting developing subject.

The workshop will focus on aspects of G2 geometry and related topics including:

  • metrics with G2 holonomy
  • calibrated submanifolds
  • gauge theory
  • connections with physics.
Confirmed speakers are:

Bobby Acharya (KCL), Simon Donaldson (IC), Anna Fino (Turin), Mark Haskins (IC), Andriy Haydys (Bielefeld), Nigel Hitchin (Oxford), Dominic Joyce (Oxford), Alexei Kovalev (Cambridge), Jason Lotay (UCL), Thomas Madsen (KCL), Johannes Nordström (IC), Simon Salamon (KCL), Thomas Walpuski (IC).

We would like to particularly encourage postdocs and graduate students to attend.

Anyone interested in attending the workshop should register with Emily Balls (emily.balls(at)kcl.ac.uk) by May 18th, providing their name, email address and institution. Attendance is free but places will be limited, so we would like to encourage early registration.

Talks will take place at King's College London on Monday and at University College London on Tuesday.

Subvariedades de codimensión dos en espaciotiempos

Granada (España)

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Con reconocimiento como actividad formativa de los programas de doctorado Matemáticas y Física y Matemáticas

Seminario de Matemáticas, 1ª Planta, Sección de Matemáticas

Conferenciantes invitados

Estrategias concretas para la mejora docente del profesorado de Ciencias e Ingeniería en el uso de las tecnologías de tipo Web 2.0

Facultad de Ciencias (Granada, España)

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Objetivo

La formación y la actualización permanente del profesorado, centrándose en acciones docentes que puedan desarrollarse con apoyo de ordenador.

Contenidos

  • Diseño de una página web orientado a la docencia I.
  • Diseño de una página web orientado a la docencia II
  • El blog como formato de apoyo a la docencia universitaria.

Destinatarios

Profesorado y becarios de investigación que figuren en el Plan de Ordenación Docente de la Universidad de Granada durante el curso 2011-12 y/o 2012-13 de la Facultad de Ciencias y las E.T.S. de Ingeniería de Edificación y de Ingenierí­a de Caminos, Canales y Puertos.

Plazo de inscripción

Del 22 mayo al 6 de junio de 2012. Para solicitar la inscripción, enviar por correo electrónico los siguientes datos: nombre y apellidos, centro de trabajo y puesto que ocupa. La inscripción se realizará por orden de llegada. Dirección de enví­o: rcamino(at)ugr.es

Requisitos

Ordenador portátil con acceso a internet y una cuenta en Google.

Recomendaciones

Tener instalado Firefox o Chrome, el editor Komodo Edit, el gestor FTP FileZilla.

Differential Geometry

Będlewo (Poland)

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The conference is planned as the fifth in the series (previous conferences in the years: 2000, 2003, 2005, 2008) of meetings organized in the framework of the BC activities by geometers from the Jagiellonian University in Cracow and Technische Universität Berlin. Since the meeting of the group of researchers from Europe, Japan, China and USA in Oberwolfach in 1986 , they have organized and attended many conferences (in various places of the world) dealing with topics connecting Riemannian (or pseudo-Riemannian) geometry, affine differential geometry (leading the topic far beyond the classical affine differential geometry), PDEs and their geometric aspects. The former conferences essentially enlarged the cooperation between mathematicians representing the above fields as well as attracted young researchers. A detailed list (with references, information about non-published partial results) of open problems was formulated during each of the above mentioned conferences. This time we are going to formulate such a list as well. A proposed list of topics of the planned meeting contains, in particular, the following:
  • Manifolds and PDEs (in particular Ricci solitons, geometric solution of the Monge-Ampère equations, solutions for certain types of PDEs via the geometric context in which they arise, nonlinear forth order PDEs which appear when studying curvature problems in affine hypersurface theory)
  • affine submanifolds (after some stagnation there have appeared new important papers in the field, for instance two spectacular papers of Z. Hu, C. Lee, H. Li, L. Vrancken, namely complete classification of all Blaschke hypersurfaces with parallel (Levi-Civita) cubic form - in case locally strongly convex (J. Diff. Geom. to appear)- in case of Lorentz metrics (RM to appear),
  • relations between submanifolds in the Riemannian and affine settings (parallel submanifolds in the sense of Hicks, Backlund related submanifolds etc.),
  • statistical and Hessian manifolds in relation with affine differential geometry,
  • submanifolds of product spaces (submanifolds with extrinsic symmetry properties, submanifolds solving some variational problems etc.),
  • affine geometry on abstract manifolds, in particular the theory of homogeneous affine connections, affine manifolds (in the sense of Auslander),
  • Weyl geometries,
  • manifolds with special structures (Sasakian, Kaehler-Norden, contact etc.),
  • curvature conditions (in particular, decomposition of curvature tensor),
  • Lagrangian and CR submanifolds (in Riemannian and affine setting) conditions in Riemannian and pseudo-Riemannian geometry)
  • Lagrangian and CR submanifolds (metric and affine)

Taller de jóvenes de la REAG

ICMAT (Cantoblanco, Madrid)

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El Taller de Análisis Geométrico es una actividad organizada por la Red Española de Análisis Geométrico (REAG) orientada a jóvenes investigadores. Siguiendo la costumbre de otros años, el Taller tendrá como ponentes a jóvenes investigadores predoctorales o con la tesis reciente, y está abierto a miembros de la REAG y a cualquier investigador trabajando en temas afines. Esperamos que las charlas sean divulgativas para este tipo de público, en un ambiente distendido que nos permita exponer y conocer las líneas de investigación que seguimos los que trabajamos en estos temas.
Participantes
  • Pablo Angulo Ardoy (UAM)
  • Matteo Galli (UGR)
  • Vincent Gimeno García (UJI)
  • Asunción Jiménez Grande (UGR)
  • Jose Miguel Manzano Prego (UGR)
  • Pere Menal (UAB)

CMC and Minimal surfaces

Granada (Spain)

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Mini curso dentro del doctorado en Matemáticas impartido por el profesor William H. Meeks III de la universidad de Amherst.

Conferenciantes invitados

Workshop on the Willmore conjecture

Granada (Spain)

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Fernando C. Marques (IMPA - Rio de Janeiro, Brazil) and André Neves (Imperial College - London, UK) have recently given a proof of the Willmore conjecture. In this workshop these authors will give a detailed survey on their proof.
Additionally, related aspects of the Willmore conjecture will be covered in the meeting.

Conferenciantes invitados

Recordando a Florentino García Santos. IX Encuentro Andaluz de Geometría

Jaén (España)

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Esta novena edición de los Encuentros Andaluces de Geometría está dedicada a la memoria de nuestro compañero Florentino García Santos. Esta vez nos reuniremos en el Parador de Jaén el día 11 de mayo de 2012. Organizados por miembros de los grupos de investigación Geometría diferencial y sus aplicaciones y Geometria (Semi) Riemanniana y Aplicaciones, habrá participantes de las Universidades de Córdoba, Granada, Málaga, Sevilla, así como de otros lugares de fuera de Andalucía, como Bilbao, Murcia o Valencia. Como en otras ocasiones, en un ambiente distendido, se impartirán charlas con las últimos avances de los participantes.

Workshop on Geometric Analysis

Goethe-Universität Frankfurt (Germany)

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The aim of the workshop is to bring together people working in Geometric Analysis.

Speakers

  • Spyros Alexakis (University of Toronto)
  • Christine Breiner (MIT)
  • Esther Cabezas-Rivas (Universität Münster)
  • Jingyi Chen (University of British Columbia)
  • Camillo De Lellis (Universität Zürich)
  • Ailana Fraser (University of British Columbia)
  • Gerhard Huisken (MPI für Gravitationsphysik Golm)
  • Yuxiang Li (Tsinghua University Beijing)
  • Andrea Malchiodi (SISSA)
  • Jan Metzger (Universität Potsdam)
  • William P. Minicozzi II (Johns Hopkins University)
  • André Neves (Imperial College London)
  • Tristan Rivière (ETH Zürich)
  • Felix Schulze (Freie Universität Berlin)
  • Jeffrey Streets (University of California, Irvine)
  • Peter Topping (University of Warwick)
  • Brian White (Stanford University)
  • Neshan Wickramasekera (University of Cambridge)

Homenaje a Florentino García Santos

Salón de Grados, Facultad de Ciencias, UGR

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El Rector de la Universidad de Granada, el Decano de la Facultad de Ciencias y el Director del Departamento de Geometría y Topología, tienen el gusto de invitarle al acto de presentación del Libro Homenaje al Profesor D. Florentino García Santos y al descubrimiento de una placa conmemorativa, que dará su nombre al Salón de Grados de la Facultad de Ciencias. Dicho acto tendrá lugar en el Salón de Grados de la Facultad de Ciencias, a las 13.00 horas.

Conferente about the Willmore conjecture

Université de Marne-la-Vallée (Paris, France)

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Andre Neves and Fernando Coda have proposed a proof of the Willmore Conjecture (posted on arxiv). L. Hauswirth and H. Rosenberg organize a day of conferences on this subject at the University of Marne-la Vallee, on Monday March 19th. We encourage all these interested to participate. If you will participate, please do write to hauswirth(at)univ-mlv.fr. Programme:
  • 09h30-10h30: Antonio Ros (Université de Grenade).La conjecture de Willmore:le cas symétrique.
  • 11h00-12h30: André Neves (Imperial College). Minmax theory and the Willmore conjecture I
  • 12h30-14h00: Déjeuner sur place
  • 14h00-15h30: André Neves (Imperial College). Minmax theory and the Willmore conjecture II
  • 16h00-17h00: Tristan Rivière (E.T.H. Zurich). Minimizers and saddle points for the Willmore energy.

Research Programme on Geometry and Quantization of Moduli Spaces

CRM Bellaterra (Barcelona)

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Scientific description

This Research Program will be centered on the study of the geometry of algebraic moduli spaces, mostly (but not exclusively) associated to compact Riemann surfaces. The scope is intended to be wide, ranging from questions on the topology (cohomology, stable homotopy, etc.) of moduli spaces to problems on their quantization (Verlinde algebra, Hitchin connection, etc.), including also problems on dynamics (e.g. action of the mapping class group of the surface), quantum cohomology (Atiyah–Floer conjecture, Geometric Langlands program) and other areas. Most of the moduli spaces to be studied in the Research Program will be either instances or related to moduli spaces of flat connections and Higgs bundles on Riemann surfaces.

Perspectives of the Programme

The central aims of the programme are to bring together experts in various aspects on the geometry and quantization of moduli spaces and related areas, to advance these topics, and to introduce research students and post-docs to the wealth of ideas and problems in them. As stated above, the interdependence of the topics we have identified is crucial to the development of the theory, and a major goal is to develop these ideas further. The programme will include an advanced course, two workshops, a final conference, as well as a regular seminar.