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Metric Curvatures Revisited: A Brief Overview

  • Emil Saucan
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2184)

Abstract

We survey metric curvatures, special accent being placed upon the Wald curvature, its relationship with Alexandrov 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.

Notes

Acknowledgements

Research partly supported by Israel Science Foundation Grants 221/07 and 93/11 and by European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement no [URI-306706].

Part of this work was done while visiting the Max Planck Institute, Leipzig. Their gracious and warm hospitality, as well as their support are gratefully acknowledged.

The author would like to thank to organizers of 2013 CIRM Meeting on Discrete Curvature for the opportunity they gave him to write this book chapter, and especially Pascal Romon for his attentive guidance and support during the process of writing this presentation, as well as of the short conference proceeding notes.

Thanks are also due to the anonymous reviewer for his attentive, insightful and most helpful corrections and suggestions.

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Authors and Affiliations

  1. 1.Electrical Engineering DepartmentTechnionHaifaIsrael
  2. 2.Mathematics DepartmentTechnionHaifaIsrael

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