English

Regularity of limit sets of AdS quasi-Fuchsian groups

Differential Geometry 2023-11-14 v2 Geometric Topology

Abstract

Limit sets of AdS\mathrm{AdS}-quasi-Fuchsian groups of PO(n,2)\mathrm{PO}(n,2) are always Lipschitz submanifolds. The aim of this article is to show that they are never C1\mathcal{C}^1, except for the case of Fuchsian groups. As a byproduct we show that AdS\mathrm{AdS}-quasi-Fuchsian groups that are not Fuchsian are Zariski dense in PO(n,2)\mathrm{PO}(n,2).

Keywords

Cite

@article{arxiv.1809.10639,
  title  = {Regularity of limit sets of AdS quasi-Fuchsian groups},
  author = {Olivier Glorieux and Daniel Monclair},
  journal= {arXiv preprint arXiv:1809.10639},
  year   = {2023}
}