A compactness result for Fano manifolds and Kähler Ricci flows

Gang Tian, Qi S. Zhang

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

We obtain a compactness result for Fano manifolds and Kähler 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 Kähler Ricci flows. One assumption is the $$C^1$$C1 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 Kähler Ricci flows. The proof is based on a Hölder estimate for the gradient of harmonic functions and mixed derivative of Green’s function.

Original languageEnglish (US)
Pages (from-to)965-999
Number of pages35
JournalMathematische Annalen
Volume362
Issue number3-4
DOIs
StatePublished - Dec 2 2015

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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