UZH-Logo

Maintenance Infos

Hyperbolic rank and subexponential corank of metric spaces


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

Abstract

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.

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.

Citations

5 citations in Web of Science®
4 citations in Scopus®
Google Scholar™

Altmetrics

Downloads

32 downloads since deposited on 29 Nov 2010
14 downloads since 12 months
Detailed statistics

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2002
Deposited On:29 Nov 2010 16:27
Last Modified:05 Apr 2016 13:25
Publisher:Birkhäuser
ISSN:1016-443X
Additional Information:The original publication is available at www.springerlink.com
Publisher DOI:https://doi.org/10.1007/s00039-002-8247-7
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1911661
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0992.54027
Permanent URL: https://doi.org/10.5167/uzh-21934

Download

[img]
Preview
Content: Accepted Version
Filetype: PDF
Size: 173kB
View at publisher

TrendTerms

TrendTerms displays relevant terms of the abstract of this publication and related documents on a map. The terms and their relations were extracted from ZORA using word statistics. Their timelines are taken from ZORA as well. The bubble size of a term is proportional to the number of documents where the term occurs. Red, orange, yellow and green colors are used for terms that occur in the current document; red indicates high interlinkedness of a term with other terms, orange, yellow and green decreasing interlinkedness. Blue is used for terms that have a relation with the terms in this document, but occur in other documents.
You can navigate and zoom the map. Mouse-hovering a term displays its timeline, clicking it yields the associated documents.

Author Collaborations