## Acta Mathematica

### Regularity of Kähler–Ricci flows on Fano manifolds

#### Abstract

In this paper, we will establish a regularity theory for the Kähler–Ricci flow on Fano n-manifolds with Ricci curvature bounded in Lp-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].

#### Note

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

#### Article information

Source
Acta Math., Volume 216, Number 1 (2016), 127-176.

Dates
First available in Project Euclid: 30 January 2017

https://projecteuclid.org/euclid.acta/1485802469

Digital Object Identifier
doi:10.1007/s11511-016-0137-1

Mathematical Reviews number (MathSciNet)
MR3508220

Zentralblatt MATH identifier
1356.53067

Rights

#### Citation

Tian, Gang; Zhang, Zhenlei. Regularity of Kähler–Ricci flows on Fano manifolds. Acta Math. 216 (2016), no. 1, 127--176. doi:10.1007/s11511-016-0137-1. https://projecteuclid.org/euclid.acta/1485802469

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