On Ptolemaic metric simplicial complexes

Details On Ptolemaic metric simplicial complexes On Ptolemaic metric simplicial complexes

2009-06-10

arxiv.org/abs/0906.1916v1

Mathematics

Metric Geometry

13 pages

Scientific paper

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.

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