Quasicircles and quasiperiodic surfaces in pseudo-hyperbolic spaces

• 成果类型: Article
• 署名作者: Labourie, Francois; Toulisse, Jeremy
• 署名单位: Universite Cote d'Azur; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-023-01182-9
• 发表日期: 2023
• 页码: 81-168
• 关键词: maximal representations

摘要

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 Teichmuller space.