Analysis & PDE

  • Anal. PDE
  • Volume 12, Number 3 (2019), 721-735.

Convergence of the Kähler–Ricci iteration

Tamás Darvas and Yanir A. Rubinstein

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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.

Article information

Anal. PDE, Volume 12, Number 3 (2019), 721-735.

Received: 15 June 2017
Revised: 27 April 2018
Accepted: 29 June 2018
First available in Project Euclid: 25 October 2018

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 32Q20: Kähler-Einstein manifolds [See also 53Cxx]
Secondary: 14J45: Fano varieties 32W20: Complex Monge-Ampère operators

Ricci iteration Kähler–Einstein metrics Fano manifolds


Darvas, Tamás; Rubinstein, Yanir A. Convergence of the Kähler–Ricci iteration. Anal. PDE 12 (2019), no. 3, 721--735. doi:10.2140/apde.2019.12.721.

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