Characterization of pinched Ricci curvature by functional
inequalities
by Li-Juan Cheng and Anton Thalmaier
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, 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
http://doi.org/10.1007/s12220-017-9905-1
The preprint version is available here:
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