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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

 

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


Author: S. Buyalo
Translated by: the author
Original publication: Algebra i Analiz, tom 17 (2005), nomer 2.
Journal: St. Petersburg Math. J. 17 (2006), 267-283
MSC (2000): Primary 53B99
Published electronically: February 10, 2006
MathSciNet review: 2159584
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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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Additional Information

S. Buyalo
Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia
Email: sbuyalo@pdmi.ras.ru

DOI: http://dx.doi.org/10.1090/S1061-0022-06-00903-4
PII: S 1061-0022(06)00903-4
Keywords: Visual Gromov hyperbolic space
Received by editor(s): November 1, 2004
Published electronically: February 10, 2006
Additional Notes: The author was supported by RFBR (grant no. 02-01-00090).
Article copyright: © Copyright 2006 American Mathematical Society