Convergence of the Weak Kähler–Ricci Flow on Manifolds of General Type-Reference-Cited by-同舟云学术

Convergence of the Weak Kähler–Ricci Flow on Manifolds of General Type

Published:2019-11-15 Issue:8 Volume:2021 Page:6373-6404
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Tô Tat Dat¹

Affiliation:

1. Ecole Nationale de l’Aviation Civile, Unversité de Toulouse, 7, Avenue Edouard Belin, FR-31055 Toulouse Cedex and Institut Mathématiques de Toulouse, Université de Toulouse, CNRS, UPS, 31062 Toulouse cedex 09, France

Abstract

Abstract We study the Kähler–Ricci flow on compact Kähler manifolds whose canonical bundle is big. We show that the normalized Kähler–Ricci flow has long-time existence in the viscosity sense, is continuous in a Zariski open set, and converges to the unique singular Kähler–Einstein metric in the canonical class. The key ingredient is a viscosity theory for degenerate complex Monge–Ampère flows in big classes that we develop, extending and refining the approach of Eyssidieux–Guedj–Zeriahi.

Funder

ANR GRACK

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

http://academic.oup.com/imrn/article-pdf/2021/8/6373/37304174/rnz256.pdf

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