A compactness result for Fano manifolds and K\"ahler Ricci flows
Differential Geometry
2014-04-16 v1 Analysis of PDEs
Abstract
We obtain a compactness result for Fano manifolds and K\"ahler Ricci flows. Comparing to the more general Riemannian versions by Anderson and Hamilton, in this Fano case, the curvature assumption is much weaker and is preserved by the K\"ahler Ricci flows. One assumption is the boundedness of the Ricci potential and the other is the smallness of Perelman's entropy. As one application, we obtain a new local regularity criteria and structure result for K\"ahler Ricci flows. The proof is based on a H\"older estimate for the gradient of harmonic functions, which may be of independent interest.
Keywords
Cite
@article{arxiv.1404.3783,
title = {A compactness result for Fano manifolds and K\"ahler Ricci flows},
author = {Gang Tian and Qi S. Zhang},
journal= {arXiv preprint arXiv:1404.3783},
year = {2014}
}