English

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

R2 v1 2026-06-23T18:09:09.274Z