English

The conical K\"ahler-Ricci flow on Fano manifolds

Differential Geometry 2015-02-03 v3

Abstract

In this paper, we study the long-term behavior of the conical K\"ahler-Ricci flow on Fano manifold MM. First, based on our work of locally uniform regularity for the twisted K\"ahler-Ricci flows, we obtain a long-time solution to the conical K\"ahler-Ricci flow by limiting a sequence of these twisted flows. Second, we study the uniform Perelman's estimates of the twisted K\"ahler-Ricci flows. After that, we prove that the conical K\"ahler-Ricci flow must converge to a conical K\"ahler-Einstein metric if there exists one.

Keywords

Cite

@article{arxiv.1402.1832,
  title  = {The conical K\"ahler-Ricci flow on Fano manifolds},
  author = {Jiawei Liu and Xi Zhang},
  journal= {arXiv preprint arXiv:1402.1832},
  year   = {2015}
}

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46 pages