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

Buyalo, S.

doi:10.1090/S1061-0022-06-00903-4

Asymptotic dimension of a hyperbolic space and capacity dimension of its boundary at infinity
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by S. Buyalo
Translated by: the author

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

DOI: https://doi.org/10.1090/S1061-0022-06-00903-4

Published electronically: February 10, 2006

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Abstract:

A quasisymmetry invariant of a metric space $Z$ (called the capacity dimension, $\operatorname {cdim} Z$) is introduced. The main result says that the asymptotic dimension of a visual Gromov hyperbolic space $X$ is at most the capacity dimension of its boundary at infinity plus 1, $\operatorname {asdim} X \le \operatorname {cdim} \partial _\infty X+1$.

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