Remote Access 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
Full-text PDF

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$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in St. Petersburg Mathematical Journal with MSC (2000): 51M10

Retrieve articles in all journals with MSC (2000): 51M10

Additional Information

S. Buyalo
Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia

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

American Mathematical Society