24 juin 2020

François Labourie (Université de Nice)
Plateau problems for maximal surfaces in pseudo-hyperbolic spaces

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Lieu : Demander le lien Zoom à jean-michel.bismut@u-psud.fr

Résumé : The pseudo-hyperbolic space $H^2,n$ is in many ways a generalisation of the hyperbolic space. It is a pseudo-Riemannian manifold with signature (2,n) with constant curvature, it also has a « boundary at infinity ». We explain in this joint work with Jérémy Toulisse and Mike Wolf how special curves in this boundary at infinity, bounds unique maximal surfaces in H^2,n. The result bears some analogy with the Cheng-Yau existence results for affine spheres tangent to convex curves in the projective plane. The talk will spend sometime explainig the geometry of the pseudo-hyperbolic space and its boundary at infinity, as well as description of maximal surfaces. If time permits, I will explain some extension to « quasi-periodic » maximal surfaces in H^2,n.

Plateau problems for maximal surfaces in pseudo-hyperbolic spaces  Version PDF