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

Metric Curvature Revisited - A Brief Overview

Emil Saucan


We survey metric curvatures, special accent being placed upon the Wald curvature, its relationship with Alexandov curvature, as well as its application in defining a metric Ricci curvature for $PL$ cell complexes and a metric Ricci flow for PL surfaces. In addition, a simple, metric way of defining curvature for metric measure spaces is proposed.

MSC Codes:
53C44, 52C26, 68U05, 65D18, 51K10, 51K10, 57R40
Metric curvature, Alexandrov curvature, metric Ricci curvature flow, snow aking operator

Related publications

2017 Repository Open Access
Emil Saucan

Metric curvatures revisited : a brief overview

In: Modern approaches to discrete curvature / Laurent Najman... (eds.)
Cham : Springer, 2017. - pp. 63-114
(Lecture notes in mathematics ; 2184)