Embedding of hyperbolic spaces in the product of trees
S. Buyalo, V. Schroeder
Abstract
We show that for each n 2 there is a quasi-isometric embedding of the hyperbolic space Hn in the product Tn=Tx...xT of n copies of a (simplicial) metric tree T. On the other hand, we prove that there is no quasi-isometric embedding H2 --> TxRm for any metric tree T and any m 0.
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