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Ricci flow on compact Kähler manifolds of positive bisectional curvature

Huai-Dong Cao·Bing-Long Chen·Xi-Ping Zhu
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Abstract

We announce a new proof of the uniform estimate on the curvature of solutions to the Ricci flow on a compact Kähler manifold $M^n$ with positive bisectional curvature. In contrast to the recent work of X. Chen and G. Tian, our proof of the uniform estimate does not rely on the exsitence of Kähler-Einstein metrics on $M^n$, but instead on the first author's Harnack inequality for the Kähler-Ricc flow, and a very recent local injectivity radius estimate of Perelman for the Ricci flow.

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Huai-Dong Cao, Bing-Long Chen, Xi-Ping Zhu. 2003-02-08. Ricci flow on compact Kähler manifolds of positive bisectional curvature. https://arxiv.org/abs/math/0302087

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