Discrete subgroups of small critical exponent

Liu, Beibei¹ ; Wang, Shi²

¹ Department of Mathematics, The Ohio State University, Columbus, OH, United States
² Institute of Mathematical Sciences, ShanghaiTech University, Shanghai, China

Geometry & topology, Tome 27 (2023) no. 6, pp. 2347-2381.

Résumé

We prove that finitely generated Kleinian groups $\Gamma <\mathrm{Isom}({ℍ}^n)$ with small critical exponent are always convex cocompact. We also prove some geometric properties for any complete pinched negatively curved manifold with critical exponent less than $1$.

Détail

DOI : 10.2140/gt.2023.27.2347

Keywords: discrete subgroups, critical exponent, convex compactness

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