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The conical Kähler-Ricci flow on Fano manifolds
Jiawei Liu, Xi Zhang, 2014.02.08
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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