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On Ptolemaic metric simplicial complexes
Published online by Cambridge University Press: 10 May 2010
Abstract
We show that under certain mild conditions, a metric simplicial complex which satisfies the Ptolemy inequality is a CAT(0) space. Ptolemy's inequality is closely related to inversions of metric spaces. For a large class of metric simplicial complexes, we characterize those which are isometric to Euclidean space in terms of metric inversions.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 149 , Issue 1 , July 2010 , pp. 93 - 104
- Copyright
- Copyright © Cambridge Philosophical Society 2010