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.
CITATION STYLE
Saucan, E. (2017). Metric curvatures revisited: A brief overview. In Lecture Notes in Mathematics (Vol. 2184, pp. 63–114). Springer Verlag. https://doi.org/10.1007/978-3-319-58002-9_2
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