Boundaries of Hyperbolic Metric Spaces
Corran Webster, Adam Winchester
Abstract
We investigate the relationship between the metric boundary and the Gromov boundary of a hyperbolic metric space. We show that the Gromov boundary is a quotient topological space of the metric boundary, and that therefore a word-hyperbolic group has an amenable action on the metric boundary of its Cayley graph. This result has significance for the study of Lip-norms on group C*-algebras.
Create a lesson
Related papers
The Bézout inequality for mixed volumes characterizes simplices
Dylan Langharst, Shouda Wang
Affine dual Minkowski problem for general measures
Cheng Zhang, Hailin Jin
Algebraically independent distances and rigid metrics
Yoshito Ishiki
On the Geometry of Wasserstein Barycenter II: Riemannian Rigidity, Essential Non-Branching, and Finsler Models
Bang-Xian Han, Deng-Yu Liu
A Weak Topology on Metric Spaces
Armando W. Gutiérrez, Olavi Nevanlinna
Uncentered Blaschke-Santaló inequalities for the Gaussian measure
S. Artstein-Avidan, M. Fradelizi, K. Wyczesany