Limit sets for convex cocompact groups in higher rank symmetric spaces

TL;DR

This paper characterizes convex cocompact groups in higher rank symmetric spaces by showing that their limit points are conical if and only if the group is convex cocompact, extending understanding of geometric group actions.

Contribution

It establishes a new equivalence between conical limit points and convex cocompactness for Zariski dense subgroups in higher rank symmetric spaces.

Findings

Limit points are conical iff the group is convex cocompact

Characterization applies to Zariski dense discrete subgroups

Extends classical results to higher rank symmetric spaces

Abstract

We show that every limit point of a Zariski dense discrete subgroup $\Gamma$ of the isometry group of a symmetric space of noncompact type is conical if and only if $\Gamma$ is convex cocompact.