Convergence of kähler-ricci flow on lower-dimensional algebraic manifolds of general type

Gang Tian; Zhenlei Zhang

doi:10.1093/imrn/rnv357

Convergence of kähler-ricci flow on lower-dimensional algebraic manifolds of general type

Gang Tian, Zhenlei Zhang

Mathematics

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

In this paper, we prove that the L⁴-norm of Ricci curvature is uniformly bounded along a Kähler-Ricci flow on any minimal algebraic manifold. As an application, we show that on any minimal algebraic manifold M of general type and with dimension n≤ 3, any solution of the normalized Kähler-Ricci flow converges to the unique singular Kähler-Einstein metric on the canonical model of M in the Cheeger-Gromov topology.

Original language	English (US)
Pages (from-to)	6493-6511
Number of pages	19
Journal	International Mathematics Research Notices
Volume	2016
Issue number	21
DOIs	https://doi.org/10.1093/imrn/rnv357
State	Published - 2016

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1093/imrn/rnv357

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title = "Convergence of k{\"a}hler-ricci flow on lower-dimensional algebraic manifolds of general type",

abstract = "In this paper, we prove that the L4-norm of Ricci curvature is uniformly bounded along a K{\"a}hler-Ricci flow on any minimal algebraic manifold. As an application, we show that on any minimal algebraic manifold M of general type and with dimension n≤ 3, any solution of the normalized K{\"a}hler-Ricci flow converges to the unique singular K{\"a}hler-Einstein metric on the canonical model of M in the Cheeger-Gromov topology.",

author = "Gang Tian and Zhenlei Zhang",

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AB - In this paper, we prove that the L4-norm of Ricci curvature is uniformly bounded along a Kähler-Ricci flow on any minimal algebraic manifold. As an application, we show that on any minimal algebraic manifold M of general type and with dimension n≤ 3, any solution of the normalized Kähler-Ricci flow converges to the unique singular Kähler-Einstein metric on the canonical model of M in the Cheeger-Gromov topology.

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Convergence of kähler-ricci flow on lower-dimensional algebraic manifolds of general type

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