Kähler-Ricci flow and Ricci iteration on log-Fano varieties

Details Kähler-Ricci flow and Ricci iteration on log-Fano varieties Kähler-Ricci flow and Ricci iteration on log-Fano varieties

2011-11-30

arxiv.org/abs/1111.7158v1

Mathematics

Complex Variables

43 pages

Scientific paper

We prove the existence and uniqueness of K\"ahler-Einstein metrics on log-Fano varieties whose Mabuchi functional is proper. We then study analogues of the works of Perelman, Tian and Zhu on the convergence of the normalized K\"ahler-Ricci flow, and of Keller, Rubinstein on its discrete version, Ricci iteration. In the special case of (smooth) Fano manifolds, our results on Ricci iteration yield smooth convergence without any additional condition, improving on previous results. Our result for the K\"ahler-Ricci flow provides weak convergence independently of Perelman's celebrated estimates.

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