Embedding of hyperbolic spaces in the product of trees
Geometric Topology
2009-06-04 v1 Metric Geometry
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.
Cite
@article{arxiv.math/0311524,
title = {Embedding of hyperbolic spaces in the product of trees},
author = {S. Buyalo and V. Schroeder},
journal= {arXiv preprint arXiv:math/0311524},
year = {2009}
}
Comments
18 pages, 2 figures