Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

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.
Document type :
Preprints, Working Papers, ...
Complete list of metadata

https://hal.archives-ouvertes.fr/hal-02991915
Contributor : François Labourie <>
Submitted on : Friday, November 6, 2020 - 10:58:19 AM
Last modification on : Saturday, November 7, 2020 - 3:26:25 AM

Links full text

Identifiers

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

Collections

Citation

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

Share

Metrics

Record views

4