论文标题
伪hyperbolic空间中的准圆和准环境表面
Quasicircles and quasiperiodic surfaces in pseudo-hyperbolic spaces
论文作者
论文摘要
我们在本文中研究了伪hyperbolic空间中的准膜状最大表面，并表明它们的特征是曲率条件，gromov双曲线或形成性双曲线。我们表明，爱因斯坦宇宙中这些表面的极限曲线承认了一个规范的准对称参数化，而相反，爱因斯坦宇宙中的每一个准对称曲线都以一种准对象参数化是持续扩展的，以使准对象的表面不断扩展。我们将这些结果应用于渐近双曲线表面，Anosov表示的刚度和通用Teichmüller空间的版本。
We study in this paper quasiperiodic maximal surfaces in pseudo-hyperbolic spaces and show that they are characterised by a curvature condition, Gromov hyperbolicity or conformal hyperbolicity. We show that the limit curves of these surfaces in the Einstein Universe admits a canonical quasisymmetric parametrisation, while conversely every quasisymmetric curve in the Einstein Universe bounds a quasiperiodic surface in such a way that the quasisymmetric parametrisation is a continuous extension of the uniformisation; we give applications of these results to asymptotically hyperbolic surfaces, rigidity of Anosov representations and a version of the universal Teichmüller space.
