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Ricci tensor on ${\rm RCD}^*(K,N)$ spaces

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arxiv 1412.0441 v4 pith:L6DRHPFV submitted 2014-12-01 math.MG

Bang-Xian Han This is my paper · ORCID
classification math.MG
keywords riccispacestensorbochnerconditioncurvature-dimensiondefinitiondimensional
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abstract

We obtain an improved Bochner inequality based on the curvature-dimension condition ${\rm RCD}^*(K,N)$ and propose a definition of $N$-dimensional Ricci tensor on metric measure spaces.

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  1. Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces

    math.MG 2019-09 conditional novelty 7.0 of 10

    In RCD(K,N) spaces, the reduced boundary of a set of finite perimeter has a unique Euclidean half-space tangent at almost every point and is rectifiable by bi-Lipschitz charts.

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