On a new definition of Ricci curvature on Alexandrov spaces

Mathematics – Differential Geometry

Scientific paper

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Scientific paper

Recently, in [49], a new definition for lower Ricci curvature bounds on
Alexandrov spaces was introduced by the authors. In this article, we extend our
research to summarize the geometric and analytic results under this Ricci
condition. In particular, two new results, the rigidity result of Bishop-Gromov
volume comparison and Lipschitz continuity of heat kernel, are obtained.

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