Boundaries of Hyperbolic Metric Spaces

Details Boundaries of Hyperbolic Metric Spaces Boundaries of Hyperbolic Metric Spaces

2003-10-08

arxiv.org/abs/math/0310101v1

Mathematics

Metric Geometry

9 pages. AMSLaTeX

Scientific paper

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.

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