On the Kahler Ricci flow on projective manifolds of general type

Abstract

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.

References in corpus (5)

• The Kahler-Ricci flow through singularities
• Gromov-Hausdorff limits of Kahler manifolds and algebraic geometry, II
• Riemannian geometry of Kahler-Einstein currents
• Riemannian geometry of Kahler-Einstein currents II: an analytic proof of Kawamata's base point free theorem
• Continuity of Extremal Transitions and Flops for Calabi-Yau Manifolds

Cited by in corpus (4)

• Bounding diameter of singular Kähler metric
• The local entropy along Ricci flow---Part A: the no-local-collapsing theorems
• Convergence of Kähler-Ricci flow on lower dimensional algebraic manifolds of general type
• The Kähler-Ricci flow on Fano bundles