Quick Search:

uzh logo
Browse by:
bullet
bullet
bullet
bullet

Zurich Open Repository and Archive

Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-21536

Foertsch, T; Lytchak, A; Schroeder, V (2007). Nonpositive curvature and the Ptolemy inequality. International Mathematics Research Notices, 2007(rnm100):online.

[img]
Preview
Accepted Version
PDF
197kB

View at publisher

Abstract

We provide examples of nonlocally, compact, geodesic Ptolemy metric spaces which are not uniquely geodesic. On the other hand, we show that locally, compact, geodesic Ptolemy metric spaces are uniquely geodesic. Moreover, we prove that a metric space is CAT(0) if and only if it is Busemann convex and Ptolemy.

Citations

7 citations in Web of Science®
13 citations in Scopus®
Google Scholar™

Altmetrics

Downloads

40 downloads since deposited on 10 Dec 2009
9 downloads since 12 months

Detailed statistics

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
DDC:510 Mathematics
Language:English
Date:2007
Deposited On:10 Dec 2009 15:55
Last Modified:14 Jan 2014 21:16
Publisher:Oxford University Press
ISSN:1073-7928
Additional Information:This is a pre-copy-editing, author-produced PDF of an article accepted for publication in International Mathematics Research Notices following peer review. The definitive publisher-authenticated version "Foertsch, T; Lytchak, A; Schroeder, V (2007). Nonpositive curvature and the Ptolemy inequality. International Mathematics Research Notices, 2007(rnm100)" is available online at: International Mathematics Research Notices
Publisher DOI:10.1093/imrn/rnm100
Related URLs:http://arxiv.org/abs/0705.1042

Users (please log in): suggest update or correction for this item

Repository Staff Only: item control page