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Embedding of hyperbolic spaces in the product of trees


Buyalo, S; Schroeder, V (2005). Embedding of hyperbolic spaces in the product of trees. Geometriae Dedicata, 113(1):75-93.

Abstract

We show that for each n\ge 2 there is a quasi-isometric embedding of the hyperbolic space H^n in the product T^n=Tx...xT of n copies of a (simplicial) metric tree T. On the other hand, we prove that there is no quasi-isometric embedding H^2 --> TxR^m for any metric tree T and any m\ge 0

Abstract

We show that for each n\ge 2 there is a quasi-isometric embedding of the hyperbolic space H^n in the product T^n=Tx...xT of n copies of a (simplicial) metric tree T. On the other hand, we prove that there is no quasi-isometric embedding H^2 --> TxR^m for any metric tree T and any m\ge 0

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:hyperbolic spaces - quasi-isometries
Language:English
Date:2005
Deposited On:08 Feb 2010 14:36
Last Modified:05 Apr 2016 13:24
Publisher:Springer
ISSN:0046-5755
Additional Information:The original publication is available at www.springerlink.com
Publisher DOI:https://doi.org/10.1007/s10711-005-3124-9

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