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Pré-Publication, Document De Travail Année : 2020

Plateau Problems for Maximal Surfaces in Pseudo-Hyperbolic Spaces

Jérémy Toulisse
  • Fonction : Auteur
Michael Wolf
  • Fonction : Auteur

Résumé

We define and prove the existence of unique solutions of an asymptotic Plateau problem for spacelike maximal surfaces in the pseudo-hyperbolic space of signature (2, n): the boundary data is given by loops on the boundary at infinity of the pseudo-hyperbolic space which are limits of positive curves. We also discuss a compact Plateau problem. The required compactness arguments rely on an analysis of the pseudo-holomorphic curves defined by the Gauss lifts of the maximal surfaces.

Dates et versions

hal-02991933 , version 1 (06-11-2020)

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François Labourie, Jérémy Toulisse, Michael Wolf. Plateau Problems for Maximal Surfaces in Pseudo-Hyperbolic Spaces. 2020. ⟨hal-02991933⟩
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