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.
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| Accepted Version 192Kb |
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.
| 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 16:55 |
| Last Modified: | 27 Nov 2012 13:34 |
| 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 |
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