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Regularity of Kähler–Ricci flows on Fano manifolds

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Acta Mathematica

Abstract

In this paper, we will establish a regularity theory for the Kähler–Ricci flow on Fano n-manifolds with Ricci curvature bounded in L p-norm for some \({p > n}\). Using this regularity theory, we will also solve a long-standing conjecture for dimension 3. As an application, we give a new proof of the Yau–Tian–Donaldson conjecture for Fano 3-manifolds. The results have been announced in [45].

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Author information

Authors and Affiliations

  1. School of Mathematical Sciences and Beijing International Center for Mathematical Research, Peking University, Beijing, 100871, China

    Gang Tian

  2. Department of Mathematics, Princeton University, Princeton, NJ, 08544, U.S.A

    Gang Tian

  3. School of Mathematics, Capital Normal University, Beijing, 100048, China

    Zhenlei Zhang

Authors
  1. Gang Tian
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  2. Zhenlei Zhang
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Corresponding author

Correspondence to Zhenlei Zhang.

Additional information

The first author was supported by NSF grants. The second author was supported by a grant of Beijing MCE 11224010007 and NSFC 13210010022.

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Tian, G., Zhang, Z. Regularity of Kähler–Ricci flows on Fano manifolds. Acta Math 216, 127–176 (2016). https://doi.org/10.1007/s11511-016-0137-1

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