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We announce a new proof of the uniform estimate on the curvature of solutionsto the Ricci flow on a compact K\"ahler manifold $M^n$ with positivebisectional 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 ofK\"ahler-Einstein metrics on $M^n$, but instead on the first author's Harnackinequality for the K\"ahler-Ricc flow, and a very recent local injectivityradius estimate of Perelman for the Ricci flow.

Ricci flow on compact Kähler manifolds of positive bisectional curvature