Regularity of Kähler–Ricci flows on Fano manifolds

Gang Tian; Zhenlei Zhang

doi:10.1007/s11511-016-0137-1

Regularity of Kähler–Ricci flows on Fano manifolds

Gang Tian, Zhenlei Zhang

Mathematics

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49 Scopus citations

Abstract

In this paper, we will establish a regularity theory for the Kähler–Ricci flow on Fano n-manifolds with Ricci curvature bounded in L^p-norm for some p> n. Using this regularity theory, we will also solve a long-standing conjecture for dimension 3. As an application, we give a new proof of the Yau–Tian–Donaldson conjecture for Fano 3-manifolds. The results have been announced in [45].

Original language	English (US)
Pages (from-to)	127-176
Number of pages	50
Journal	Acta Mathematica
Volume	216
Issue number	1
DOIs	https://doi.org/10.1007/s11511-016-0137-1
State	Published - Mar 1 2016

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s11511-016-0137-1

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abstract = "In this paper, we will establish a regularity theory for the K{\"a}hler–Ricci flow on Fano n-manifolds with Ricci curvature bounded in Lp-norm for some p> n. Using this regularity theory, we will also solve a long-standing conjecture for dimension 3. As an application, we give a new proof of the Yau–Tian–Donaldson conjecture for Fano 3-manifolds. The results have been announced in [45].",

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Regularity of Kähler–Ricci flows on Fano manifolds

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