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Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-21934

Buyalo, S; Schroeder, V (2002). Hyperbolic rank and subexponential corank of metric spaces. Geometric and Functional Analysis, 12(2):293-306.

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We introduce a new quasi-isometry invariant corank X of a metric space X called subexponential corank. A metric space X has subexponential corank k if roughly speaking there exists a continuous map , T is a topological space, such that for each the set g -1(t) has subexponential growth rate in X and the topological dimension dimT = k is minimal among all such maps. Our main result is the inequality for a large class of metric spaces X including all locally compact Hadamard spaces, where rank h X is the maximal topological dimension of among all CAT(—1) spaces Y quasi-isometrically embedded into X (the notion introduced by M. Gromov in a slightly stronger form). This proves several properties of rank h conjectured by Gromov, in particular, that any Riemannian symmetric space X of noncompact type possesses no quasi-isometric embedding of the standard hyperbolic space H n with n – 1 > dim X – rank X.

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
DDC:510 Mathematics
Deposited On:29 Nov 2010 16:27
Last Modified:17 Dec 2013 10:39
Additional Information:The original publication is available at www.springerlink.com
Publisher DOI:10.1007/s00039-002-8247-7
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1911661
Citations:Web of Science®. Times Cited: 5
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Scopus®. Citation Count: 4

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