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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

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.

Received:
06.06.14
Published:
10.06.14
MSC Codes:
51F99, 53B20, 52C99
Keywords:
Comparison geometry, geodesic space, Kirszbraun's theorem, Nonpositive curvature

Related publications

inJournal
2015 Repository Open Access
Miroslav Bačák, Bobo Hua, Jürgen Jost, Martin Kell and Armin Schikorra

A notion of nonpositive curvature for general metric spaces

In: Differential geometry and its applications, 38 (2015), pp. 22-32