Open Access
2018 Kähler–Ricci flow, Kähler–Einstein metric, and K–stability
Xiuxiong Chen, Song Sun, Bing Wang
Geom. Topol. 22(6): 3145-3173 (2018). DOI: 10.2140/gt.2018.22.3145


We prove the existence of a Kähler–Einstein metric on a K–stable Fano manifold using the recent compactness result on Kähler–Ricci flows. The key ingredient is an algebrogeometric description of the asymptotic behavior of Kähler–Ricci flow on Fano manifolds. This is in turn based on a general finite-dimensional discussion, which is interesting on its own and could potentially apply to other problems. As one application, we relate the asymptotics of the Calabi flow on a polarized Kähler manifold to K–stability, assuming bounds on geometry.


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Xiuxiong Chen. Song Sun. Bing Wang. "Kähler–Ricci flow, Kähler–Einstein metric, and K–stability." Geom. Topol. 22 (6) 3145 - 3173, 2018.


Received: 19 October 2015; Revised: 27 February 2018; Accepted: 27 March 2018; Published: 2018
First available in Project Euclid: 29 September 2018

zbMATH: 06945124
MathSciNet: MR3858762
Digital Object Identifier: 10.2140/gt.2018.22.3145

Primary: 53C25 , 53C44
Secondary: 14J45

Keywords: convergence , Fano manifold , Kähler Ricci flow , K–stability , uniqueness

Rights: Copyright © 2018 Mathematical Sciences Publishers

Vol.22 • No. 6 • 2018
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