Discrete subgroups of small critical exponent
Differential Geometry
2023-09-06 v2 Group Theory
Geometric Topology
Abstract
We prove that finitely generated higher dimensional Kleinian groups with small critical exponent are always convex-cocompact. Along the way, we also prove some geometric properties for any complete pinched negatively curved manifold with critical exponent less than 1.
Keywords
Cite
@article{arxiv.2008.12365,
title = {Discrete subgroups of small critical exponent},
author = {Beibei Liu and Shi Wang},
journal= {arXiv preprint arXiv:2008.12365},
year = {2023}
}
Comments
This version is accepted for publication in G&T. We added more details in the proofs of Corollary 1.6, Lemma 3.5 and Theorem 3.7. We also improved the exposition