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arXiv · 0811.0991

A note on compact Kähler-Ricci flow with positive bisectional curvature

Huai-Dong Cao·Meng Zhu
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Abstract

We show that for any solution to the Kähler-Ricci flow with positive bisectional curvature on a compact Kähler manifold $M^n$, the bisectional curvature has a uniform positive lower bound. As a consequence, the solution converges exponentially fast to an Kähler-Einstein metric with positive bisectional curvature as t tends to the infinity, provided we assume the Futaki-invariant of $M^n$ is zero. This improves a result of D. Phong, J. Song, J. Sturm and B. Weinkove in which they assumed the stronger condition that Mabuchi K-energy is bounded from below.

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Huai-Dong Cao, Meng Zhu. 2008-11-20. A note on compact Kähler-Ricci flow with positive bisectional curvature. https://arxiv.org/abs/0811.0991

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