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Characterizations of monotonicity of vector fields on metric measure spaces

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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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Authors and Affiliations

  1. Institute for Applied Mathematics, University of Bonn, Endenicher Allee 60, 53115, Bonn, Germany

    Bang-Xian Han

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  1. Bang-Xian Han
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Correspondence to Bang-Xian Han.

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Communicated by L. Ambrosio.

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Han, BX. Characterizations of monotonicity of vector fields on metric measure spaces. Calc. Var. 57, 113 (2018). https://doi.org/10.1007/s00526-018-1388-9

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  • DOI: https://doi.org/10.1007/s00526-018-1388-9

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