Capacity dimension and embedding of hyperbolic spaces into a product of trees
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S. Buyalo
Translated by: the author - St. Petersburg Math. J. 17 (2006), 581-591
- DOI: https://doi.org/10.1090/S1061-0022-06-00921-6
- Published electronically: May 3, 2006
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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
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Bibliographic Information
- S. Buyalo
- Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia
- 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)
- © Copyright 2006 American Mathematical Society
- Journal: St. Petersburg Math. J. 17 (2006), 581-591
- MSC (2000): Primary 51M10
- DOI: https://doi.org/10.1090/S1061-0022-06-00921-6
- MathSciNet review: 2173936