Non-positive curvature and the Ptolemy inequality

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We provide examples of non-locally 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.
11 pages, 2 figures

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Metric Geometry, 53C20

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http://salesiana.dossiersoluciones.com/handle/123456789/128574

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0705.1042
 http://arxiv.org/abs/0705.1042

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arXiv