A notion of nonpositive curvature for general metric spaces

Miroslav Bačák, Bobo Hua, Jürgen Jost, Martin Kell, and Armin Schikorra

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Submission date: 06. Jun. 2014
Pages: 13
published in: Differential geometry and its applications, 38 (2015), p. 22-32 
DOI number (of the published article): 10.1016/j.difgeo.2014.11.002
Bibtex
MSC-Numbers: 51F99, 53B20, 52C99
Keywords and phrases: Comparison geometry, geodesic space, Kirszbraun's theorem, Nonpositive curvature
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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.