Regularity of limit sets of AdS quasi-Fuchsian groups

Abstract

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