TY - JOUR
T1 - A compactness result for Fano manifolds and Kähler Ricci flows
AU - Tian, Gang
AU - Zhang, Qi S.
N1 - Publisher Copyright:
© 2014, Springer-Verlag Berlin Heidelberg.
PY - 2015/12/2
Y1 - 2015/12/2
N2 - 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.
AB - 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.
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U2 - 10.1007/s00208-014-1147-y
DO - 10.1007/s00208-014-1147-y
M3 - Article
AN - SCOPUS:84937517947
SN - 0025-5831
VL - 362
SP - 965
EP - 999
JO - Mathematische Annalen
JF - Mathematische Annalen
IS - 3-4
ER -