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 Kahler-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.

References in corpus (2)

• Some discretizations of geometric evolution equations and the Ricci iteration on the space of Kahler metrics, I
• On energy functionals, Kahler-Einstein metrics, and the Moser-Trudinger-Onofri neighborhood

Cited by in corpus (2)

• On the Ricci iteration for homogeneous metrics on spheres and projective spaces
• Ricci iteration for coupled Kähler-Einstein metrics