Asymptotic dimension of a hyperbolic space and capacity dimension of its boundary at infinity

Details Asymptotic dimension of a hyperbolic space and capacity dimension of its boundary at infinity Asymptotic dimension of a hyperbolic space and capacity dimension of its boundary at infinity

2005-05-20

arxiv.org/abs/math/0505427v1

St. Petersbg Math. J. 17 (2006), 267-283

Mathematics

Geometric Topology

23 pages

Scientific paper

We introduce a quasi-symmetry invariant of a metric space Z called the
capacity dimension. Our main result says that for a visual Gromov hyperbolic
space X the asymptotic dimension of X is at most the capacity dimension of its
boundary at infinity plus 1.

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