Title: 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.