On Ptolemaic metric simplicial complexes
Metric Geometry
2015-05-13 v1
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.
Cite
@article{arxiv.0906.1916,
title = {On Ptolemaic metric simplicial complexes},
author = {S. M. Buckley and J. McDougall and D. J. Wraith},
journal= {arXiv preprint arXiv:0906.1916},
year = {2015}
}
Comments
13 pages