Maximal surfaces in anti-de Sitter 3-manifolds with particles
Annales de l'Institut Fourier, Volume 66 (2016) no. 4, p. 1409-1449

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 π. 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 π.

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 π. 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 π.

Received : 2014-05-05
Revised : 2015-09-18
Accepted : 2015-11-15
Published online : 2016-07-28
Classification:  53C42,  53C50
Keywords: maximal surfaces, cone-manifolds, Lorentz geometry, minimal Lagrangian maps
     author = {Toulisse, J\'er\'emy},
     title = {Maximal surfaces in anti-de Sitter 3-manifolds with particles},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {66},
     number = {4},
     year = {2016},
     pages = {1409-1449},
     doi = {10.5802/aif.3040},
     language = {en},
     url = {}
Toulisse, Jérémy. Maximal surfaces in anti-de Sitter 3-manifolds with particles. Annales de l'Institut Fourier, Volume 66 (2016) no. 4, pp. 1409-1449. doi : 10.5802/aif.3040.

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