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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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