%0 Generic %1 Bonsante2009 %A Bonsante, Francesco %A Schlenker, Jean-Marc %D 2009 %K maximal surfaces teichmuller universal %T Maximal surfaces and the universal Teichm"uller space %U http://arxiv.org/abs/0911.4124 %X We show that any element of the universal Teichm"uller 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.

@misc{Bonsante2009, abstract = { We show that any element of the universal Teichm\"uller 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. }, added-at = {2010-12-09T19:28:01.000+0100}, author = {Bonsante, Francesco and Schlenker, Jean-Marc}, biburl = {https://www.bibsonomy.org/bibtex/293a72fa0db9352e66854d6495b8ccb12/uludag}, description = {Maximal surfaces and the universal Teichm\"uller space}, interhash = {f8897dedb7c98ae607e42109d0b2b392}, intrahash = {93a72fa0db9352e66854d6495b8ccb12}, keywords = {maximal surfaces teichmuller universal}, note = {cite arxiv:0911.4124 Comment: 31 pages, 3 figures}, timestamp = {2010-12-09T19:28:01.000+0100}, title = {Maximal surfaces and the universal Teichm\"uller space}, url = {http://arxiv.org/abs/0911.4124}, year = 2009 }