On the Kahler Ricci flow on projective manifolds of general type

We consider the Kähler Ricci flow on a smooth minimal model of general type, we show that if the Ricci curvature is uniformly bounded below along the Kähler-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 (\cite{TZ}) that if the canonical line bundle $K_X$ is big and nef, but not ample, then the flow is of Type IIb.

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