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math.GT2004
Hyperbolic dimension of metric spaces
S. Buyalo, V. Schroeder
We introduce a new quasi-isometry invariant of metric spaces called the hyperbolic dimension, hypdim, which is a version of the Gromov's asymptotic dimension, asdim. The hyperbolic…
math.GT2003
Embedding of hyperbolic spaces in the product of trees
S. Buyalo, V. Schroeder
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 h…