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Embedding of hyperbolic spaces in the product of trees

S. Buyalo·V. Schroeder
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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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S. Buyalo, V. Schroeder. 2003-11-28. Embedding of hyperbolic spaces in the product of trees. https://arxiv.org/abs/math/0311524

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