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1.
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 AdS3, 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. 相似文献
2.
Masahiro YANAGISHITA 《数学学报(英文版)》2014,(4)
Being a Strebel point gives a sufficient condition for that the extremal Beltrami coefficient is uniquely determined in a Teichmüller equivalence class.We consider how Strebel points are characterized.In this paper,we will give a new characterization of Strebel points in a certain subset of the universal Teichmüller space by a property of the Grunsky operator. 相似文献
3.
万有Teichmüler空间T是所有规范的拟对称同胚组成的集合.在Bers嵌入下,T与Δ上共形映射的Schwarz导数密切相关.本文讨论由规范的对称同胚所组成的子集T0的相应性质. 相似文献