Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hyperbolic dimension of metric spaces   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 dimension is at most the asymptotic dimension,
however, unlike the asymptotic dimension, the hyperbolic dimension of any
Euclidean space R^n is zero (while asdim R^n=n.) This invariant possesses usual
properties of dimension like monotonicity and product theorems. Our main result
says that the hyperbolic dimension of any Gromov hyperbolic space X (with mild
restrictions) is at least the topological dimension of the boundary at infinity
plus 1. As an application we obtain that there is no quasi-isometric embedding
of the real hyperbolic space H^n into the (n-1)-fold metric product of metric
trees stabilized by any Euclidean factor.

23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex