Maximal surfaces and the universal Teichmüller space - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Inventiones Mathematicae Année : 2010

Maximal surfaces and the universal Teichmüller space

Francesco Bonsante
  • Fonction : Auteur
  • PersonId : 914147

Résumé

We show that any element of the universal Teichmüller space is realized by a unique minimal Lagrangian diffeomorphism from the hyperbolic plane to itself. The proof uses maximal surfaces in the 3-dimensional anti-de Sitter space. We show that, in $AdS^{n+1}$, any subset $E$ of the boundary at infinity which is the boundary at infinity of a space-like hypersurface bounds a maximal space-like hypersurface. In $AdS^3$, if $E$ is the graph of a quasi-symmetric homeomorphism, then this maximal surface is unique, and it has negative sectional curvature. As a by-product, we find a simple characterization of quasi-symmetric homeomorphisms of the circle in terms of 3-dimensional projective geometry.

Dates et versions

hal-00618944 , version 1 (04-09-2011)

Identifiants

Citer

Francesco Bonsante, Jean-Marc Schlenker. Maximal surfaces and the universal Teichmüller space. Inventiones Mathematicae, 2010, 182 (2), pp.279-333. ⟨10.1007/s00222-010-0263-x⟩. ⟨hal-00618944⟩
93 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More