Acta Mathematica

Regularity of Kähler–Ricci flows on Fano manifolds

Gang Tian and Zhenlei Zhang

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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].


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

Received: 22 October 2013
First available in Project Euclid: 30 January 2017

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2016 © Institut Mittag-Leffler


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.

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