Metric Curvature Revisited - A Brief Overview
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Submission date: 14. Jul. 2014 (revised version: October 2016)
published in: Modern approaches to discrete curvature / L. Najman ... (eds.)
Cham : Springer, 2017. - P. 63 - 114
(Lecture notes in mathematics ; 2184)
DOI number (of the published article): 10.1007/978-3-319-58002-9_2
MSC-Numbers: 53C44, 52C26, 68U05, 65D18, 51K10, 51K10, 57R40
Keywords and phrases: Metric curvature, Alexandrov curvature, metric Ricci curvature flow, snow aking operator
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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.