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.
"Convergence of the Kähler–Ricci iteration." Anal. PDE 12 (3) 721 - 735, 2019. https://doi.org/10.2140/apde.2019.12.721