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Geometriae Dedicata

, Volume 113, Issue 1, pp 75–93 | Cite as

Embedding of Hyperbolic Spaces in the Product of Trees

  • Sergei Buyalo
  • Viktor Schroeder
Article

Abstract

We show that for each n ≥ 2 there is a quasi-isometric embedding of the hyperbolic space H n in the product T n =T × ··· × T of n copies of a (simplicial) metric tree T. On the other hand, we prove that there is no quasi-isometric embedding \(H^{2} \rightarrow T\times \mathbb{R}^{m}\) for any metric tree T and any m ≥ 0.

Keywords

hyperbolic spaces quasi-isometries 

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References

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Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.St. Petersburg Dept. of SteklovMath. Institute RASSt. PetersburgRussia
  2. 2.Institut für MathematikUniversität ZürichZürichSwitzerland

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