MiS Preprint Repository

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 ( 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

Topology and curvature of metric spaces

Parvaneh Joharinad and Jürgen Jost


We develop a new concept of non-positive curvature for metric spaces, based on intersection patterns of closed balls. In contrast to the synthetic approaches of Alexandrov and Busemann, our concept also applies to metric spaces that might be discrete. The natural comparison spaces that emerge from our discussion are no longer Euclidean spaces, but rather tripod spaces. These tripod spaces include the hyperconvex spaces which have trivial Čech homology. This suggests a link of our geometrical method to the topological method of persistent homology employed in topological data analysis. We also investigate the geometry of general tripod spaces.

Apr 1, 2019
Apr 1, 2019
Curvature inequality, discrete metric space, hyperconvex, hyperbolic, intersection of balls, tripod

Related publications

2019 Repository Open Access
Parvaneh Joharinad and Jürgen Jost

Topology and curvature of metric spaces

In: Advances in mathematics, 356 (2019), p. 106813