## Analysis & PDE

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

### Convergence of the Kähler–Ricci iteration

#### Abstract

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

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

Dates
Revised: 27 April 2018
Accepted: 29 June 2018
First available in Project Euclid: 25 October 2018

https://projecteuclid.org/euclid.apde/1540432868

Digital Object Identifier
doi:10.2140/apde.2019.12.721

Mathematical Reviews number (MathSciNet)
MR3864208

Zentralblatt MATH identifier
06986451

#### Citation

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. https://projecteuclid.org/euclid.apde/1540432868

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