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# Superficies de Curvatura Media Anisotrópica Constante

## Marcos Paulo Tassi Universidade Federal de São Carlos

En esa charla hablaremos sobre las superficies de curvatura media anisotrópica constante (superficies CMAC), que surgen como puntos críticos (con o sin restricción a las variaciones que preservan el volumen) del funcional de área anisotrópica, dado por la integral de una función suave definida sobre la esfera y evaluada sobre la aplicación de Gauss de la superficie. Un caso particular de superficies CMAC ocurre cuando la función de anisotropía es idénticamente igual a 1, correspondiendo a las superficies mínimas y de curvatura media constante (superficies CMC).
Al igual que las superficies CMC, las superficies CMAC también se presentan localmente como grafos de soluciones de una ecuación diferencial cuasi-lineal elíptica, lo que nos permite su estudio bajo la luz del Principio del Máximo.
Presentaremos los conceptos introductorios de la teoría y algunos resultados obtenidos, como estimaciones uniformes de altura para grafos CMAC con borde plano, con aplicación al estudio de superficies propiamente embebidas con topología finita, y un teorema de tipo Bernstein para multigrafos CMAC completos.

Seminario 1ª planta, IEMath-GR

# Index and nullity of Lawson surfaces

## Nikolaos Kapouleas University of Brown

I will discuss recent work with David Wiygul to determine the index and nullity of the Lawson surfaces $\xi_{g,1}$ (in Lawson's original notation) of any genus $g\ge2$ (arXiv:1904.05812).

Seminario 1ª planta, IEMath-GR

# The Calabi-Yau problem for Riemann surfaces with finite genus and countably many ends

## Franc Forstneric Univerza v Ljubljani

We show that if R is a compact Riemann surface and M is a domain in R whose complement is a union of countably many pairwise disjoint smoothly bounded closed discs, then M is the complex structure of a complete bounded minimal surface in $\mathbb{R}^3$. More precisely, we prove that there is a complete conformal minimal immersion $X:M→\mathbb{ℝ}^3$ extending to a continuous map from the closure of $M$ such that $X(\partial M)$ is a union of pairwise disjoint Jordan curves. This extends a result for finite bordered Riemann surfaces proved in 2015. (Joint work with Antonio Alarcon.)

Seminario 1ª planta, IEMath-GR

# Asimptotic Plateau problem for prescribed mean curvature hypersurfaces

## Ilkka Holopainen University of Helsinki

I will talk on a recent joint preprint with Jean-Baptiste Casteras and Jaime Ripoll. We prove the existence of solutions to the asymptotic Plateau problem for hypersurfaces of prescribed mean curvature in Cartan-Hadamard manifolds N. More precisely, given a suitable subset L of the asymptotic boundary of N and a suitable function H on N, we are able to construct a set of locally finite perimeter whose boundary has generalized mean curvature H and asymptotic boundary L provided that N satisfies the so-called strict convexity condition and that its sectional curvatures are bounded from above by a negative constant. We also obtain a multiplicity result in low dimensions.

Seminario de la primera planta, IEMathUGR

# Superficies CMC de género arbitrario en $\mathbb{M}^2(\epsilon) \times \mathbb{R}$

Se presentará una extensión de la técnica conjugada de Plateau para la construcción de superficies de curvatura media constante en espacios homogéneos. Usando dicha técnica se construirán superficies de curvatura media constante compactas de género arbitrario simétricas con respecto al grupo de simetrías de una teselación de $\mathbb{M}^2(\epsilon) \times \mathbb{R}$ para H menor que cierta cota superior que depende de la teselación. En el caso $\mathbb{S}^2\times \mathbb{R}$ (i.e. $\epsilon=1$) se probará que dichas superficies son embebidas para $H < 1/2$.

Seminario 1ª planta, IEMath-GR

# Scherk-like translators for the Mean Curvature Flow

We prove existence and uniqueness for a two-parameter family of translators for mean curvature flow. We get additional examples by taking limits at the boundary of the parameter space. Some of the translators resemble well-known minimal surfaces (Scherk's doubly periodic minimal surfaces, helicoids), but others have no minimal surface analogs. This is a joint work with D. Hoffman and B. White.

Seminario 1ª planta, IEMath-GR

# The wedge theorem for ancient mean curvature flows

## Niels Martin Moller University of Copenhagen

We show that a wedge theorem (also called a bi-halfspace theorem) holds for properly immersed ancient solutions to the mean curvature flow in n-dimensional Euclidean space. This adds to a long story, as it generalizes our own wedge theorem for self-translators from 2018, which implies the minimal surface case by Hoffman-Meeks (1990) that in turn contains the classical cone theorem by Omori (1967). Another application of the wedge theorem is to classify the convex hulls of the sets of reach of all proper ancient flows, hence posing restrictions on the possible singularities that can occur in mean curvature flow. The proof uses a parabolic Omori-Yau maximum principle for proper ancient flows. This is joint work with Francesco Chini (Univ. Copenhagen).

Seminario 1ª Planta, IEMATH

# Jenkins-Serrin problem for translating graphs

I will discuss about recent joint works with E.S. Gama, J. de Lira and F. Martín concerning Jenkins-Serrin type problems for the graphical translators of the mean curvature flow in Riemannian product manifolds $M\times R$. We prove, for example, the existence of Jenkins-Serrin type translators that can be described as horizontal graphs "over" suitable domains in a vertical plane.

# Some results of invariant theory for CR-manifolds

## Yen-Chang Huang Xinyang Normal University

In this talk, I will introduce some recent works of invariant theory on CR manifolds. After a briefing of CR manifolds, some integral invariants will be introduced in the Heisenberg groups (regarded as a flat model of CR manifolds). The invariants are not changed in the sense of the pseudo-hermitian transformations which can be regarded as the rigid motions in the Heisenberg groups. We take the approach from Integral Geometry for convex bodies, but in our case, the assumption of convexity is not necessary. The applications can be implemented to the CR-version of the Crofton's formula and the containment problems with other related. Some recent development in the invariant theory for CR manifolds will also be discussed in the end of the talk.

Seminario 1ª planta, IEMath-GR

# Isoparametric surfaces in $\mathbb{E}(\kappa,\tau)$-spaces

We provide an explicit classification of the following four families of surfaces in any homogeneous 3-manifold with 4-dimensional isometry group:

• isoparametric surfaces,
• surfaces with constant principal curvatures,
• extrinsically homogeneous surfaces,
• $H$-surfaces with vanishing Abresch-Rosenberg differential.
This is a joint work with Miguel Domínguez Vázquez.

Seminario 1ª planta, IEMath-GR

# Carleman type theorems in complex analysis and minimal surface theory

## Brett Chenoweth Universidad de Liubliana

Carleman’s approximation theorem (1927) was ostensibly the first result concerning approximation of continuous functions defined on an unbounded closed set of C, namely R, by entire functions. The approximation is stronger than uniform approximation as the error at x can be made to taper off as x approaches infinity (from within R). An essential property of R for such an approximation to exist is that it has bounded exhaustion hulls, that is, the complement of R in the one point compactification of C is locally connected at infinity. Bounded exhaustion hulls play an important role in the characterisation of totally real sets admitting Carleman approximation and Carleman approximation of jets; see Manne et al (2011), Magnusson and Wold (2016). In this talk I will discuss some recent generalisations of Carleman’s theorem including preliminary results from ongoing joint work with Ildefonso Castro-Infantes where the problem of approximating by directed holomorphic immersions, for example by null curves, is being considered.

Seminario de la primera planta, IEMath

# Geometric Analysis, Submanifolds, and Geometry of PDE's

## Turín (Italia)

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The conference will focus on three strongly correlated themes: geometric analysis, geometry of submanifolds and geometry of PDEs, bringing together leading mathematicians in the field. The conference will consist of 16 plenary lectures and of invited lectures in parallel sessions. A poster session will be also scheduled aside of the main activities.

# XXVIII International Fall Workshop on Geometry and Physics

## ICMAT (Spain)

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The Fall Workshops on Geometry and Physics have been held yearly since 1992, and bring together Spanish and Portuguese geometers and physicists, along with an ever increasing number of participants from outside the Iberian Peninsula. The meetings aim to provide a forum for the exchange of ideas between researchers of different fields in Differential Geometry, Applied Mathematics and Physics, and always include a substantial number of enthusiastic young researchers amongst the participants.

# Advances and Challenges in Nonlinear Analysis ... and Beyond!

## Bari (Italia)

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This international conference will give us the opportunity to celebrate our good friend Vieri Benci’s 70th birthday.

Vieri is a brilliant mathematician who has authored or co-authored several books and about two hundred papers published on international scientific journals and both his teaching and his passion for research have contributed to the training of many students who have then pursued an academic career in Mathematics.

This workshop will address Vieri’s main research interests which range from variational and topological methods applied to the study of nonlinear differential equations arising in Mathematical Physics, General Relativity, Differential Geometry, to the foundations of Mathematics and Logic.

The meeting will take place from September 24 to September 27, 2019, in Bari (Italy), at the Department of Mathematics of the Università degli Studi di Bari Aldo Moro and at the Politecnico di Bari, in the university campus “Ernesto Quagliariello”.

# Seminario de análisis geométrico en la UJA

## Jaén

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Seminario de 10 horas, repartido en dos días de duración, dirigido a los alumnos del Programa Interuniversitario Matemáticas (UGR, UCA, UMA, UAL y UJA). El tema común es el Análisis Geométrico, que es una de las líneas de in- vestigación del Programa de Doctorado y es incluso el título del Proyecto MTM en el que están enrolados los ponentes del Seminario. El objetivo es transmitir de manera clara y fluida al potencial alumnado los avances en los problemas recientes de investigación básica que están abordando los ponentes en esta línea de investigación.

Se organiza en 5 sesiones teórico-prácticas de dos horas de duración cada una, impartidas por profesorado de la UJA y externo involucrados en la citada línea de investigación, incluyendo profesorado doctor reciente que transmitirá la evolución del proceso de la investigación llevada a cabo en sus tesis doctorales a los actuales alumnos del Programa de Doctorado.

Inscripciones vía email a icastro(at)ujaen.es

## Barcelona (España)

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Curso de verano en la UAB.
Curso de introducción a la investigación para alumnos de último curso de grado que hayan cursado geometría diferencial o variedades diferenciables. El curso se impartirá del 8 al 19 de julio en el campus de la UAB, Barcelona. La participación se realiza a través de becas de viaje+alojamiento que se pueden solicitar hasta el 25 de marzo. Las clases serán impartidas por Roberto Rubio. El curso está organizado por la UAB y financiando por el proyecto Marie Sklodowska-Curie GENERALIZED.

# Encuentro Iberoamericano de Geometría en Granada

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Encuentro Iberoamericano de Geometría en Granada.

# Variational Problems and the Geometry of Submanifolds

## Marsella (Francia)

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This conference will gather specialists of variational problems and the geometry of Riemannian and Lorentzian submanifolds. It will be the occasion to listen to some of the foremost researchers on harmonic maps, minimal surfaces, constant mean curvature surfaces, the Willmore problem, biharmonic maps, knot theory (from the geometric perspective), Yang-Mills theory as well as submanifolds from the viewpoint of Riemannian or Lorentzian geometry. Emphasis will be placed on young researchers, post-doctoral and Ph.D. students, who will be able to present their work.

# Bringing Young Mathematicians Together

## ICMAT (Spain)

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Welcome to the 2nd BYMAT Conference – Bringing Young Mathematicians Together. This conference aims to:
• Strengthen the links between PhD students in all disciplines where mathematics is relevant, nationally and internationally.
• Encourage researchers of different institutions, disciplines and countries to start building a network of contacts soon into their careers.
• Provide a warm and open space for researchers in the early stages of their career to present their work to peers of similar experience.
• Promote cross-disciplinary training during the PhD stage, favouring interaction with students from different areas, and boosting scientific outreach and the transfer of knowledge between academia and industry.
• Favour the use of English as a working language to make BYMAT an inclusive conference.

The conference is especially directed at PhD students in all areas of mathematics and related disciplines, and indeed any young people who use mathematics in their daily lives/jobs. Everyone, from undergraduates to university professors or industry professionals, is more than welcome to attend!

We expect contributed talks and posters to come mainly from PhD students, young industry professionals, master’s students and recent PostDoc. The official language of the conference will be English. We will have short talks (15-20 minutes), distributed in thematic parallel sessions, a poster session, 7 plenary talks given by young professors and industry professionals, workshops and plenty of social activities.

Registration is open until 30th April. Talk and grant applications can be submitted until 11th March.

# Topics in Geometric Analysis

## Princeton (USA)

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The Women and Mathematics Program (WAM) at the Institute for Advanced Study is an annual program with the mission to recruit and retain more women in mathematics. WAM aims to counter the initial imbalance in the numbers of men and women entering mathematics training as well as the higher attrition rate of female mathematicians compared to their male counterparts at every critical transition stage in mathematical careers. WAM encourages female mathematicians to form collaborative research relationships and to become active in a vertical mentoring network spanning a continuum from undergraduates to emerita professors, which provides support and reduces the sense of isolation experienced by many women in mathematics. While there are a number of women's programs targeted solely at undergraduates, or graduate students, or postdocs, very few programs provide the depth and breadth that come from simultaneously including features tailored for undergraduate students, graduate students, and researchers from a broad spectrum of US institutions, all in one united community of scholars, as WAM does.

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# Taller y Encuentro de la Red Española de Análisis Geométrico

## Murcia (España)

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El encuentro de investigadores de la REAG es una de las actividades programadas de la Red Española de Análisis Geométrico. Sus objetivos principales son favorecer el intercambio de ideas y fomentar la cooperación entre investigadores, tanto miembros de la Red como de grupos afines cuya investigación se desarrolla en el campo del Análisis Geométrico.

Esta edición se celebrará en la Universidad de Murcia. Durante los días 8 y 9 de abril tendrá lugar el taller de jóvenes investigadores donde los siguientes miembros impartirán una serie de conferencias

• Verónica L. Cánovas (Universidad de Murcia).
• Juan Luis Durán (Universidad Autónoma de Barcelona).
• Ixchel Gutiérrez Rodríguez (Universidad de Santiago de Compostela).
• David Iglesias (Universidad de Murcia).
• Erik Sarrión (Universidad Jaume I).
• Miriam Tárraga (Universidad de Murcia).

Tras el taller se celebrará el día 10 de abril el encuentro de la REAG donde los siguientes investigadores impartirán una conferencia:

• Marcos Dajczer (IMPA, Rio de Janeiro, Brasil).
• Pablo Mira (Universidad Politécnica de Cartagena).
• Roberto Rubio (Universidad Autónoma de Barcelona).

# IX Workshop on Differential Geometry

## Maceió (Brazil)

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The Workshop on Differential Geometry of the Institute of Mathematics of the Federal University of Alagoas has become a traditional event that takes place every year in Maceio-Alagoas, during the Brazilian summer. The aim of this workshop is to gather in Maceio national and international researchers of high scientific level in the field of differential geometry. In this 9th edition, the event will be held in two weeks. From 11 to 15 March, the activities will occur on the Mathematics Institute of the Federal University of Alagoas, and the program is dedicated to young researchers and graduate students, including a minicourse, 30min contributed talks and two sections of open problems. From 18 to 22 March, the activities will occur at Hotel Ponta Verde at Praia do Francês and keeps the traditional program with one minicourse and invited lectures.

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