On the Kahler Ricci flow on projective manifolds of general type

2015/01/17 by Guo, Bin · 4 citations
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1501.04239

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 (\citeTZ) 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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• Fano Fibrations and Twisted Kähler-Einstein Metrics II: The Kähler-Ricci Flow
• Fano Fibrations and Twisted Kähler-Einstein Metrics I
• Stability of asymptotically conical gradient Kähler-Ricci expanders
• Green's function estimates for compact Kähler manifolds and applications

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