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.
Cite
@article{arxiv.2010.05704,
title = {Quasicircles and quasiperiodic surfaces in pseudo-hyperbolic spaces},
author = {François Labourie and Jérémy Toulisse},
journal= {arXiv preprint arXiv:2010.05704},
year = {2022}
}
Comments
References updated, some typos corrected, 77 pages, 6 figures. Theorem A of the previous version was partly known to Cheng Qing-Min