[Surfaces maximales dans les variétés anti-de Sitter de dimension à particules]
On démontre l’existence d’une unique surface maximale dans les variétés anti-de Sitter (AdS) globalement hyperboliques maximales (GHM) à particules (c’est à dire, avec des singularités coniques le long de courbes de type temps) lorsque les angles sont inférieurs à . On interprète ce résultat en termes de théorie de Teichmüller et nous démontrons l’existence d’un unique difféomorphisme minimal lagrangien isotope à l’identité entre deux surfaces hyperboliques à singularités coniques, lorsque les angles singuliers sont les mêmes pour les deux surfaces et sont inférieurs à .
We prove the existence of a unique maximal surface in each anti-de Sitter (AdS) Globally Hyperbolic Maximal (GHM) manifold with particles (that is, with conical singularities along time-like lines) for cone angles less than . We interpret this result in terms of Teichmüller theory, and prove the existence of a unique minimal Lagrangian diffeomorphism isotopic to the identity between two hyperbolic surfaces with cone singularities when the cone angles are the same for both surfaces and are less than .
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Keywords: maximal surfaces, cone-manifolds, Lorentz geometry, minimal Lagrangian maps
Mot clés : surfaces maximales, variétés à singularités coniques, géometrie lorentzienne, applications minimales lagrangiennes
Toulisse, Jérémy 1
@article{AIF_2016__66_4_1409_0,
author = {Toulisse, J\'er\'emy},
title = {Maximal surfaces in anti-de {Sitter} 3-manifolds with particles},
journal = {Annales de l'Institut Fourier},
pages = {1409--1449},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {66},
number = {4},
year = {2016},
doi = {10.5802/aif.3040},
language = {en},
url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3040/}
}
TY - JOUR AU - Toulisse, Jérémy TI - Maximal surfaces in anti-de Sitter 3-manifolds with particles JO - Annales de l'Institut Fourier PY - 2016 SP - 1409 EP - 1449 VL - 66 IS - 4 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3040/ DO - 10.5802/aif.3040 LA - en ID - AIF_2016__66_4_1409_0 ER -
%0 Journal Article %A Toulisse, Jérémy %T Maximal surfaces in anti-de Sitter 3-manifolds with particles %J Annales de l'Institut Fourier %D 2016 %P 1409-1449 %V 66 %N 4 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3040/ %R 10.5802/aif.3040 %G en %F AIF_2016__66_4_1409_0
Toulisse, Jérémy. Maximal surfaces in anti-de Sitter 3-manifolds with particles. Annales de l'Institut Fourier, Tome 66 (2016) no. 4, pp. 1409-1449. doi : 10.5802/aif.3040. https://aif.centre-mersenne.org/articles/10.5802/aif.3040/
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