On the critical exponent of a discrete group of hyperbolic isometries
type: Item
instance of: scholarly article
title: On the critical exponent of a discrete group of hyperbolic isometries
zbMATH Open document ID: 0885.53044
DOI: 10.1016/S0926-2245(96)00051-4
author: Frédéric Paulin
published in: Differential Geometry and its Applications
publication date: 1997-09-15T00:00:00Z
review text: Generalizing work of Bishop-Jones in the constant curvature case, we prove that if \(M\) is a complete Riemannian manifold with pinched negative curvature and with \(\pi_1 M\) not virtually nilpotent, then the visual dimension of the set of geodesic rays, starting from a fixed based point, that are recurrent in some compact subset of \(M\), is equal to the critical exponent of \(\pi_1 M\). We also prove that the critical exponent of an infinite subgroup \(H\) of a given word hyperbolic group equals the visual dimension of the canonical limit set of \(H\).
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 1060720
zbMATH Keywords: recurrence
zbMATH Keywords: hyperbolic groups
zbMATH Keywords: fundamental group
zbMATH Keywords: Riemannian manifold
zbMATH Keywords: negative curvature
zbMATH Keywords: geodesic rays
zbMATH Keywords: canonical limit set
Wikidata QID: Q115337585
MaRDI profile type: Publication
cites work: Hausdorff dimension and Kleinian groups
cites work: Discrete parabolic groups
cites work: Q5565773
cites work: Sur les groupes hyperboliques d'après Mikhael Gromov. (On the hyperbolic groups à la M. Gromov)
cites work: Q3772406
cites work: Un Groupe Hyperbolique Est Déterminé Par Son Bord
cites work: Q4055870
cites work: The density at infinity of a discrete group of hyperbolic motions
description: scientific article; zbMATH DE number 1060720