Vol. 12, No. 3, 2019

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Convergence of the Kähler–Ricci iteration

Tamás Darvas and Yanir A. Rubinstein

Vol. 12 (2019), No. 3, 721–735

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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Ricci iteration, Kähler–Einstein metrics, Fano manifolds
Mathematical Subject Classification 2010
Primary: 32Q20
Secondary: 14J45, 32W20
Received: 15 June 2017
Revised: 27 April 2018
Accepted: 29 June 2018
Published: 7 October 2018
Tamás Darvas
Department of Mathematics
University of Maryland
College Park, MD
United States
Yanir A. Rubinstein
Department of Mathematics
University of Maryland
College Park, MD
United States