On the Kähler Ricci Flow on Projective Manifolds of General Type

Abstract

We consider the Käahler-Ricci flow on a smooth minimal model of general type, we show that if the Ricci curvature is uniformly bounded below along the Käahler-Ricci flow, then the diameter is uniformly bounded. As a corollary we show that under the Ricci curvature lower bound assumption, the Gromov-Hausdorff limit of the flow is homeomorphic to the canonical model. Moreover, we can give a purely analytic proof of a recent result of Tosatti-Zhang [28] that if the canonical line bundle KX is big and numerically effective, but not ample, then the flow is of Type IIb.