Normalizer, divergence type, and Patterson measure for discrete groups of the Gromov hyperbolic space

DOI10.4171/GGD/548MaRDI QIDQ784887

Yasuhiro Yabuki, Johannes Jaerisch, Katsuhiko Matsuzaki

Publication date: 3 August 2020

Published in: Groups, Geometry, and Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.02664

zbMATH Keywords

Poincaré seriesdiscrete groupergodic actionGromov hyperbolic spacenormal subgroupPatterson measuredivergence typeconical limit setproper conjugationquasiconformal measureshadow lemma

Mathematics Subject Classification ID

Geometric group theory (20F65) Hyperbolic groups and nonpositively curved groups (20F67) Kleinian groups (aspects of compact Riemann surfaces and uniformization) (30F40)

Related Items (8)

Stable random fields, Patterson-Sullivan measures and extremal cocycle growth ⋮ Local limit theorems in relatively hyperbolic groups II: the non-spectrally degenerate case ⋮ Critical exponents of invariant random subgroups in negative curvature ⋮ Growth and cogrowth of normal subgroups of a free group ⋮ Cogrowth for group actions with strongly contracting elements ⋮ Cubulating random quotients of hyperbolic cubulated groups ⋮ Entropy and drift for word metrics on relatively hyperbolic groups ⋮ Entropy and drift for Gibbs measures on geometrically finite manifolds

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The density at infinity of a discrete group of hyperbolic motions
• Géométrie et théorie des groupes. Les groupes hyperboliques de Gromov. (Geometry and group theory. The hyperbolic groups of Gromov)
• Patterson-Sullivan measures on the boundary of a hyperbolic space in the sense of Gromov
• The Poincaré series and the conformal measure of conical and Myrberg limit points
• Remarks on Hausdorff dimensions for transient limits sets of Kleinian groups
• A lower bound for the exponent of convergence of normal subgroups of Kleinian groups
• A Fatou theorem for conformal densities with applications to Galois coverings in negative curvature
• No proper conjugation for quasiconvex cocompact groups of Gromov hyperbolic spaces
• The Patterson–Sullivan measure and proper conjugation for Kleinian groups of divergence type
• Discrete conformal groups and measurable dynamics
• Ergodicité et équidistribution en courbure négative
• Cogrowth for group actions with strongly contracting elements
• Geometry and Dynamics in Gromov Hyperbolic Metric Spaces

This page was built for publication: Normalizer, divergence type, and Patterson measure for discrete groups of the Gromov hyperbolic space