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Quasicircles and quasiperiodic surfaces in pseudo-hyperbolic spaces

Abstract : 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 Teichm\"uller space.
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Preprints, Working Papers, ...
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Contributor : François Labourie <>
Submitted on : Friday, November 6, 2020 - 10:58:19 AM
Last modification on : Saturday, November 7, 2020 - 3:26:25 AM

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  • HAL Id : hal-02991915, version 1
  • ARXIV : 2010.05704



François Labourie, Jérémy Toulisse. Quasicircles and quasiperiodic surfaces in pseudo-hyperbolic spaces. 2020. ⟨hal-02991915⟩



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