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. 1.
No takes yet. Share an insight, caveat, or question.
Webster et al. (2005) studied this question.
Synapse has enriched 2 closely related papers on similar clinical questions. Consider them for comparative context: