Characterizations of monotonicity of vector fields on metric measure spaces
Functional Analysis
2021-08-17 v3 Differential Geometry
Metric Geometry
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.
Keywords
Cite
@article{arxiv.1710.07953,
title = {Characterizations of monotonicity of vector fields on metric measure spaces},
author = {Bang-Xian Han},
journal= {arXiv preprint arXiv:1710.07953},
year = {2021}
}