Characterization of pinched Ricci curvature by functional inequalities
by Li-Juan Cheng and Anton Thalmaier

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, Lp-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.

J. Geom. Analysis 28  (2018), no. 3, 2312-2345

The preprint version is available here:

Li Juan Cheng
Anton Thalmaier

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