Kähler-Einstein metrics and the Kähler-Ricci flow on log Fano varieties
Journal article, 2019

We prove the existence and uniqueness of Kähler-Einstein metrics on Q-Fano varieties with log terminal singularities (and more generally on log Fano pairs) whose Mabuchi functional is proper. We study analogues of the works of Perelman on the convergence of the normalized Kähler-Ricci flow, and of Keller, Rubinstein on its discrete version, Ricci iteration. In the special case of (non-singular) Fano manifolds, our results on Ricci iteration yield smooth convergence without any additional condition, improving on previous results. Our result for the Kähler-Ricci flow provides weak convergence independently of Perelman's celebrated estimates.


Robert Berman

Chalmers, Mathematical Sciences, Algebra and geometry

Sebastien Boucksom

École polytechnique

Philippe Eyssidieux

Institut Universitaire de France

Viincent Guedj

Institut Universitaire de France

Ahmed Zeriahi

Paul Sabatier University

Journal für die Reine und Angewandte Mathematik

0075-4102 (ISSN)

Vol. 2019 751 27-89

Subject Categories

Computational Mathematics


Mathematical Analysis


Basic sciences



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