Kähler-Einstein metrics and the Kähler-Ricci flow on log Fano varieties
Artikel i vetenskaplig tidskrift, 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.

Författare

Robert Berman

Chalmers, Matematiska vetenskaper, Algebra och geometri

Sebastien Boucksom

Centre de Mathematiques Laurent Schwartz Ecole polytechnique

Philippe Eyssidieux

Institut Universitaire de France

Viincent Guedj

Institut Universitaire de France

Ahmed Zeriahi

Universite Paul Sabatier Toulouse III

Journal für die Reine und Angewandte Mathematik

0075-4102 (ISSN)

Vol. 2019 751 27-89

Ämneskategorier

Beräkningsmatematik

Geometri

Matematisk analys

Fundament

Grundläggande vetenskaper

DOI

10.1515/crelle-2016-0033

Mer information

Senast uppdaterat

2019-07-15