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

 

Capacity dimension and embedding of hyperbolic spaces into a product of trees


Author: S. Buyalo
Translated by: the author
Original publication: Algebra i Analiz, tom 17 (2005), nomer 4.
Journal: St. Petersburg Math. J. 17 (2006), 581-591
MSC (2000): Primary 51M10
Published electronically: May 3, 2006
MathSciNet review: 2173936
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Abstract | References | Similar Articles | Additional Information

Abstract: It is proved that every visual Gromov hyperbolic space $ X$ whose boundary at infinity has finite capacity dimension, $ \operatorname{cdim}(\partial_{\infty} X)<\infty$, admits a quasiisometric embedding into an $ n$-fold product of metric trees with $ n=\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

DOI: http://dx.doi.org/10.1090/S1061-0022-06-00921-6
PII: S 1061-0022(06)00921-6
Keywords: Visual Gromov hyperbolic space, asymptotic dimension, capacity dimension
Received by editor(s): March 9, 2005
Published electronically: May 3, 2006
Additional Notes: Partially supported by RFBR (grant no. 05-01-00939) and by NSH (grant no. 1914.2003.1)
Article copyright: © Copyright 2006 American Mathematical Society