Perelman's local injectivity radius estimate and the Kaehler-Ricci flow

An important open problem in the study of the Ricci flow on compact Kaehler manifolds is whether a solution to the normalized flow is nonsingular. In this talk I will show how to combine the recent local injectivity radius estimate of Perelman with Li-Yau-Hamilton estimate to derive uniform curvature estimate for solutions to the Ricci flow on compact Kaehler manifolds with positive bisectional curvature, that is, the solution must be nonsingular. This is a joint work with B. L. Chen and X. P. Zhu.