Welcome to the Geometry Seminar of the Deparment of Geometry and Topology of the University of Granada. Here you can find information about the talks and events organized by the department.

Next talks

Unicidad del cilindro grim reaper en \(R^n\)

Universidade Federal do Ceará

Obtenemos un teorema de caracterización del cilindro construido sobre una curva grim reaper como el único solitón de traslación del flujo por la curvatura media en el espacio euclídeo \(R^n\) que es asintótico a dos hiperplanos fuera de un cilindro. Esto generaliza a dimensión arbitraria un resultado previo de Martin-Perez-Savas-Smoczyk para solitones de \(R^3\).

Seminario 2ª Planta, IEMATH

Asymptotic Dirichlet problems for the mean curvature operator

Universidad de Helsinki

In \(R^n\) (\(n\) at most 7) the famous Bernstein's theorem states that every entire solution to the minimal graph equation must be affine. Moreover, entire positive solutions in \(R^n\) are constant in every dimension by a result due to Bombieri, De Giorgi and Miranda. If the underlying space is changed from \(R^n\) to a negatively curved Riemannian manifold, the situation is completely different. Namely, if the sectional curvature of \(M\) satisfies suitable bounds, then \(M\) possess a wealth of solutions.
One way to study the existence of entire, continuous, bounded and non-constant solutions, is to solve the asymptotic Dirichlet problem on Cartan-Hadamard manifolds. In this talk I will discuss about recent existence results for minimal graphs and f-minimal graphs. The talk is based on joint works with Jean-Baptiste Casteras and Ilkka Holopainen.

Seminario 1ª Planta, IEMATH

On the topology of surfaces with the simple lift property

Motivated by the work of Colding and Minicozzi and Hoffman and White on minimal laminations obtained as limits of sequences of properly embedded minimal disks, Bernstein and Tinaglia introduce the concept of the simple lift property. Interest in these surfaces arises because leaves of a minimal lamination obtained as a limit of a sequence of properly embedded minimal disks satisfy the simple lift property. Bernstein and Tinaglia prove that an embedded minimal surface \(\Sigma\subset\Omega\) with the simple lift property must have genus zero, if \(\Omega\) is an orientable three-manifold satisfying certain geometric conditions. In particular, one key condition is that \(\Omega\) cannot contain closed minimal surfaces. In this work, I generalize this result by taking an arbitrary orientable three-manifold \(\Omega\) and proving that one is able to restrict the topology of an arbitrary surface \(\Sigma\subset\Omega\) with the simple lift property. Among other things, I prove that the only possible compact surfaces with the simple lift property are the sphere and the torus in the orientable case, and the connected sum of up to four projective planes in the non-orientable case. In the particular case where \(\Sigma\subset\Omega\) is a leaf of a minimal lamination obtained as a limit of a sequence of properly embedded minimal disks, we are able to sharpen the previous result, so that the only possible compact leaves are the torus and the Klein bottle.

Seminario 1ª planta, IEmath

Lyapounov functions for cone fields

University of Bochum

I will introduce Lyapounov functions for cone fields, a generalization of the causal structure of a Lorentzian metric, and present some results on their existence. If time permits I will define a notion of global hyperbolicity for cone fields and give a result on the existence of steep Lyapounov functions for globally hyperbolic cone fields. The material is a cooperation with Patrick Bernard (Paris).

Seminario 1ª Planta, IEMATH

Geodesic completeness of compact Lorentzian manifolds

University of Adelaide

A semi-Riemannian manifold is geodesically complete (or for short, complete) if its maximal geodesics are defined for all times. For Riemannian metrics the compactness of the manifold implies completeness. In contrast, there Lorentzian metrics on the torus that are not complete. Nevertheless, completeness plays an important role for fundamental geometric questions in Lorentzian geometry such as the classification of compact Lorentzian symmetric spaces and in particular for a Lorentzian version of Bieberbach's theorem. We will study the completeness for compact manifolds that arise from the classification of Lorentzian holonomy groups, which we will briefly review in the talk. These manifolds have abelian holonomy and carry a parallel null vector field. By determining their universal cover we show that they are complete. In the talk we will explain this result and further work in progress, both being joint work with A. Schliebner (Humboldt-University Berlin).

Seminario 1ª Planta, IEMATH

Visitors

Instituto de Matemáticas, Universidad Nacional Autónoma de México

Despacho: D4, IEMath

Universidade Federal de São Carlos

Despacho: IEMath B8-B

Next visitors

International Centre for Theoretical Sciences

Despacho: 5, segunda planta

University of Adelaide

Despacho: IEMath, despacho D5

University of Bochum

Despacho: IEMath, despacho D6

Université Paris 6

Despacho: IEMath, D11

Show more visitors

Next events

Show more events