Ricci flow on compact Kähler manifolds of positive bisectional curvature

Details Ricci flow on compact Kähler manifolds of positive bisectional curvature Ricci flow on compact Kähler manifolds of positive bisectional curvature

2003-02-08

arxiv.org/abs/math/0302087v1

Mathematics

Differential Geometry

4 pages

Scientific paper

We announce a new proof of the uniform estimate on the curvature of solutions to the Ricci flow on a compact K\"ahler 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 K\"ahler-Einstein metrics on $M^n$, but instead on the first author's Harnack inequality for the K\"ahler-Ricc flow, and a very recent local injectivity radius estimate of Perelman for the Ricci flow.

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