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Convergence of the
Kähler–Ricci iteration
Tamás Darvas and Yanir A. Rubinstein |
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Vol. 12 (2019), No. 3, 721–735
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Abstract |
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The Ricci iteration is a discrete analogue of the Ricci flow. According to Perelman, the Ricci flow converges to a Kähler–Einstein metric whenever one exists, and it has been conjectured that the Ricci iteration should behave similarly. This article confirms this conjecture. As a special case, this gives a new method of uniformization of the Riemann sphere. |
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Keywords
Ricci iteration, Kähler–Einstein metrics, Fano manifolds
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Mathematical Subject Classification 2010
Primary: 32Q20
Secondary: 14J45, 32W20
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Milestones
Received: 15 June 2017
Revised: 27 April 2018
Accepted: 29 June 2018
Published: 7 October 2018
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Authors |
| Tamás Darvas | |
| Department of Mathematics University of Maryland College Park, MD United States |
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| Yanir A. Rubinstein | |
| Department of Mathematics University of Maryland College Park, MD United States |
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