Characterizations of monotonicity of vector fields on metric measure spaces
arXiv:1710.07953 · doi:10.1007/s00526-018-1388-9
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.