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Plateau Problems for Maximal Surfaces in Pseudo-Hyperbolic Spaces

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-02991933
Contributor : François Labourie <>
Submitted on : Friday, November 6, 2020 - 11:01:21 AM
Last modification on : Saturday, November 7, 2020 - 3:26:25 AM

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  • HAL Id : hal-02991933, version 1
  • ARXIV : 2006.12190

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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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