Conical Kähler–Ricci flows on Fano manifolds

Jiawei Liu,Xi Zhang

doi:10.1016/j.aim.2016.12.002

Conical Kähler–Ricci flows on Fano manifolds

Jiawei Liu, Xi Zhang

Open Access

https://doi.org/10.1016/j.aim.2016.12.002

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Journal: Advances in Mathematics	Publication Date: Dec 27, 2016
Citations: 16	License type: publisher-specific-oa

Affiliation: University of Science and Technology of China, Chinese Academy of Sciences

#Ricci Flows #Fano Manifolds + Show 3 more

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Abstract

In this paper, we study the long-term behavior of conical Kähler–Ricci flows on Fano manifolds. First, by proving uniform regularities for twisted Kähler–Ricci flows, we prove the existence of conical Kähler–Ricci flows by limiting these twisted flows. Second, we obtain uniform Perelman's estimates along twisted Kähler–Ricci flows by improving the original proof. After that, we prove that if there exists a conical Kähler–Einstein metric, then conical Kähler–Ricci flow must converge to it.

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