Ricci flow on compact Kahler manifolds of positive bisectional curvature

This Note announces a new proof of the uniform estimate on the curvature of metric solutions to the Ricci flow on a compact Kahler manifold with positive bisectional curvature. This proof does not pre-suppose the existence of a Kahler-Einstein metric on the manifold, unlike the recent work of XiuXiong Chen and Gang Tian. It is based on the Harnack inequality for the Ricci-Kahler flow (see Invent. Math. 10 (1992) 247-263), and also on an estimation of the injectivity radius for the Ricci flow, obtained recently by Perelman.