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Characterizations of monotonicity of vector fields on metric measure spaces (1710.07953v3)
Published 22 Oct 2017 in math.FA, math.DG, and math.MG
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' andvolume cone implies metric cone theorem' in non-smooth context.
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