Convergence of weak Kähler-Ricci Flows on minimal models of positive Kodaira dimension

Abstract

Studying the behavior of the Kähler-Ricci flow on mildly singular varieties, one is naturally lead to study weak solutions of degenerate parabolic complex Monge-Ampère equations. In this article, the third of a series on this subject, we study the long term behavior of the normalized Kähler-Ricci flow on mildly singular varieties of positive Kodaira dimension, generalizing results of Song and Tian who dealt with smooth minimal models.

The proof of the parabolic comparison principle in the previous version was incorrect. We provide here a different approach which yields an alternative proof of the global comparison principle in the ample locus

References in corpus (2)

• The Kähler-Ricci flow, Ricci-flat metrics and collapsing limits
• The Kahler-Ricci flow through singularities

Cited by in corpus (2)

• Variation of singular Kähler-Einstein metrics: positive Kodaira dimension
• Relative Kähler-Einstein metric on Kähler varieties of positive Kodaira dimension