A notion of nonpositive curvature for general metric spaces☆

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Abstract

We introduce a new definition of nonpositive curvature in metric spaces and study its relation to the existing notions of nonpositive curvature in comparison geometry. The main feature of our definition is that it applies to all metric spaces and does not rely on geodesics. Moreover, a scaled and a relaxed version of our definition are appropriate in discrete metric spaces, and are believed to be of interest in geometric data analysis.

MSC

primary
51F99
53B20
secondary
52C99

Keywords

Comparison geometry
Geodesic space
Kirszbraun's theorem
Nonpositive curvature

Cited by (0)

☆

The research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement No. FP7-267087.

1

Current address: School of Mathematical Sciences, LMNS, Fudan University, Shanghai 200433, China.

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