Reference : Maximal Surface in AdS convex GHM 3-manifold with particles
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Maximal Surface in AdS convex GHM 3-manifold with particles
Toulisse, Jérémy mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
[en] AdS geometry ; minimal maps ; Teichmüller theory
[en] We prove the existence of a unique maximal surface in an anti-de Sitter (AdS) convex Globally Hyperbolic Maximal (GHM) manifold with particles (i.e. with conical singularities along timelike lines) for cone-angles less than $\pi$. We reinterpret this result in terms of Teichm\"uller theory, and prove the existence of a unique minimal Lagrangian diffeomorphism isotopic to the identity between two hyperbolic structures with conical singularities of the same angles on a closed surface with marked points.

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