Characterization of pinched Ricci curvature by functional inequalities
Probability
2016-11-08 v1
Abstract
In this article, functional inequalities for diffusion semigroups on Riemannian manifolds (possibly with boundary) are established, which are equivalent to pinched Ricci curvature, along with gradient estimates, -inequalities and log-Sobolev inequalities. These results are further extended to differential manifolds carrying geometric flows. As application, it is shown that they can be used in particular to characterize general geometric flow and Ricci flow by functional inequalities.
Keywords
Cite
@article{arxiv.1611.02160,
title = {Characterization of pinched Ricci curvature by functional inequalities},
author = {Li-Juan Cheng and Anton Thalmaier},
journal= {arXiv preprint arXiv:1611.02160},
year = {2016}
}