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

Author(s): S. Buyalo
Translated by: the author
Original publication: Algebra i Analiz, tom 17 (2005), vypusk 4.
Journal: St. Petersburg Math. J. 17 (2006), 581-591.
MSC (2000): Primary 51M10
Posted: May 3, 2006
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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$.

References:

[As]
P. Assouad, Plongements lipschitziens dans $ R^n$, Bull. Soc. Math. France 111 (1983), 429-448. MR 0763553 (86f:54050)

[BoS]
M. Bonk and O. Schramm, Embeddings of Gromov hyperbolic spaces, Geom. Funct. Anal. 10 (2000), no. 2, 266-306. MR 1771428 (2001g:53077)

[Bu]
S. V. Buyalo, Asymptotic dimension of the hyperbolic space and the capacity dimension of its boundary at infinity, Algebra i Analiz 17 (2005), no. 2, 70-95; English transl. in St. Petersburg Math. J. 17 (2006), no. 2. MR 2159584 (2006d:31009)

[BS1]
S. Buyalo and V. Schroeder, Embedding of hyperbolic spaces in the product of trees, arXive:math. GT/0311524 (2003).

[BS2]
-, Hyperbolic dimension of metric spaces, arXive:math. GT/0404525 (2004).

[Dr]
A. Dranishnikov, On hypersphericity of manifolds with finite asymptotic dimension, Trans. Amer. Math. Soc. 355 (2003), 155-167. MR 1928082 (2003g:53055)

[DZ]
A. Dranishnikov and M. Zarichnyi, Universal spaces for asymptotic dimension, Topology Appl. 140 (2004), 203-225; arXive:math. GT/0211069 (2002). MR 2074917 (2005e:54032)

[He]
J. Heinonen, Lectures on analysis on metric spaces, Universitext, Springer-Verlag, New York, 2001. MR 1800917 (2002c:30028)

[LS]
U. Lang and T. Schlichenmaier, Nagata dimension, quasisymmetric embeddings and Lipschitz extensions, arXive:math. MG/0410048 (2004).

[Ro]
J. Roe, Lectures on coarse geometry, Univ. Lecture Ser., vol. 31, Amer. Math. Soc., Providence, RI, 2003. MR 2007488 (2004g:53050)

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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: 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): 9/MAR/2005
Posted: May 3, 2006
Additional Notes: Partially supported by RFBR (grant no. 05-01-00939) and by NSH (grant no. 1914.2003.1)
Copyright of article: Copyright 2006, American Mathematical Society

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