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Regularity of Kähler–Ricci flows on Fano manifolds

Gang Tian School of Mathematical Sciences and Beijing International Center for Mathematical Research, Peking University Zhenlei Zhang School of Mathematics, Capital Normal University

Differential Geometry mathscidoc:1701.10006

Acta Mathematica, 216, (1), 127-176, 2013.10
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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@inproceedings{gang2013regularity,
  title={Regularity of Kähler–Ricci flows on Fano manifolds},
  author={Gang Tian, and Zhenlei Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203406323492813},
  booktitle={Acta Mathematica},
  volume={216},
  number={1},
  pages={127-176},
  year={2013},
}
Gang Tian, and Zhenlei Zhang. Regularity of Kähler–Ricci flows on Fano manifolds. 2013. Vol. 216. In Acta Mathematica. pp.127-176. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203406323492813.
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