English

On the Kahler Ricci flow on projective manifolds of general type

Differential Geometry 2015-01-20 v1

Abstract

We consider the K\"ahler Ricci flow on a smooth minimal model of general type, we show that if the Ricci curvature is uniformly bounded below along the K\"ahler-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 KXK_X is big and nef, but not ample, then the flow is of Type IIb.

Keywords

Cite

@article{arxiv.1501.04239,
  title  = {On the Kahler Ricci flow on projective manifolds of general type},
  author = {Bin Guo},
  journal= {arXiv preprint arXiv:1501.04239},
  year   = {2015}
}