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

Jiawei Liu; Xi Zhang

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arXiv · 1402.1832

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

Jiawei Liu·Xi Zhang

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Abstract

In this paper, we study the long-term behavior of the conical K\"ahler-Ricci flow on Fano manifold $M$. 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.

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BibTeX RIS

Jiawei Liu, Xi Zhang. 2014-02-08. The conical K\"ahler-Ricci flow on Fano manifolds. https://arxiv.org/abs/1402.1832

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