On the structure of complete Kähler manifolds with nonnegative curvature

We shall first discuss solutions of heat equation with plurisubharmonic initial data on complete Kähler manifolds with nonnegative curvature. Then we shall apply the results to study structure of this class of manifolds. We shall also discuss some properties of Kähler­Ricci flow on complete Kähler manifolds with nonnegative curvature and its relation to the uniformization conjecture by Yau which states that a complete noncompact Kähler manifold with positive holomorphic bisectional curvature is biholomorphic to ${{\mathbb C}^{n}}$.