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arXiv · 1710.07953

Characterizations of monotonicity of vector fields on metric measure spaces

Bang-Xian Han
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Abstract

We characterize the convexity of functions and the monotonicity of vector fields on metric measure spaces with Riemannian Ricci curvature bounded from below. Our result offers a new approach to deal with some rigidity theorems such as `splitting theorem' and `volume cone implies metric cone theorem' in non-smooth context.

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BibTeXRIS

Bang-Xian Han. 2017-10-22. Characterizations of monotonicity of vector fields on metric measure spaces. https://doi.org/10.1007/s00526-018-1388-9

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