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MiS Preprint
57/2014
A notion of nonpositive curvature for general metric spaces
Miroslav Bačák, Bobo Hua, Jürgen Jost, Martin Kell and Armin Schikorra
Abstract
We introduce a new defifinition of nonpositive curvature in metric spaces and study its relationship to the existing notions of nonpositive curvature in comparison geometry. The main feature of our defifinition is that it applies to all metric spaces and does not rely on geodesics. Moreover, a scaled and a relaxed version of our defifinition are appropriate in discrete metric spaces, and are believed to be of interest in geometric data analysis.