Regularity of K\"ahler-Ricci flow

Gang Tian; Zhenlei Zhang

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arXiv · 1304.2651

Regularity of K\"ahler-Ricci flow

Gang Tian·Zhenlei Zhang

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Abstract

In this short note we announce a regularity theorem for K\"ahler-Ricci flow on a compact Fano manifold (K\"ahler manifold with positive first Chern class) and its application to the limiting behavior of K\"ahler-Ricci flow on Fano 3-manifolds. Moreover, we also present a partial $C^0$ estimate to the K\"ahler-Ricci flow under the regularity assumption, which extends previous works on K\"ahler-Einstein metrics and shrinking K\"ahler-Ricci solitons (cf. \cite{Ti90}, \cite{DoSu12}, \cite{Ti12}, \cite{PSS12}). The detailed proof will appear in \cite{TiZh13}.

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Gang Tian, Zhenlei Zhang. 2013-04-09. Regularity of K\"ahler-Ricci flow. https://arxiv.org/abs/1304.2651

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