Abstract
We obtain a compactness result for Fano manifolds and Kahler Ricci flows. Comparing to the more general Riemannian versions in Anderson (Invent Math 102(2):429–445, 1990) and Hamilton (Am J Math 117:545–572, 1995), in this Fano case, the curvature assumption is much weaker and is preserved by the Kahler Ricci flows. One assumption is the $$C^1$$ 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 Kahler Ricci flows. The proof is based on a Holder estimate for the gradient of harmonic functions and mixed derivative of Green’s function.
Submitted Version (
Free)
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
