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Kähler–Ricci flow,
Kähler–Einstein metric, and K–stability
Xiuxiong Chen, Song Sun and Bing Wang |
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Geometry & Topology 22 (2018) 3145–3173
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Abstract |
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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. |
Keywords
Kähler Ricci flow, convergence, uniqueness, Fano manifold,
K–stability
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Mathematical Subject Classification 2010
Primary: 53C25, 53C44
Secondary: 14J45
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References |
Publication
Received: 19 October 2015
Revised: 27 February 2018
Accepted: 27 March 2018
Published: 23 September 2018
Proposed: Simon Donaldson
Seconded: Frances Kirwan, Bruce Kleiner
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Authors |
| Xiuxiong Chen | |
| School of Mathematics University of Science and Technology of China Hefei, Anhui China |
Department of Mathematics Stony Brook University Stony Brook, NY United States |
| http://www.math.stonybrook.edu/~xiu/ | |
| Song Sun | |
| Department of Mathematics University of California, Berkeley Berkeley, CA United States |
Department of Mathematics Stony Brook University Stony Brook, NY United States |
| https://math.berkeley.edu/people/faculty/song-sun | |
| Bing Wang | |
| School of Mathematics University of Science and Technology of China Hefei, Anhui China |
Department of Mathematics University of Wisconsin-Madison Madison, WI United States |
| http://www.math.wisc.edu/~bwang/ | |
