On Ptolemaic metric simplicial complexes
2010 ◽
Vol 149
(1)
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pp. 93-104
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Keyword(s):
AbstractWe 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.
Keyword(s):
2012 ◽
Vol 55
(1)
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pp. 157-163
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Keyword(s):
2016 ◽
Vol 08
(03)
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pp. 399-429
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