The Chern-Ricci flow on smooth minimal models of general type

Abstract

We show that on a smooth Hermitian minimal model of general type the Chern-Ricci flow converges to a closed positive current on M. Moreover, the flow converges smoothly to a Kahler-Einstein metric on compact sets away from the null locus of K_M. This generalizes work of Tsuji and Tian-Zhang to Hermitian manifolds, providing further evidence that the Chern-Ricci flow is a natural generalization of the Kahler-Ricci flow.

References in corpus (1)

• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds

Cited by in corpus (11)

• Inoue surfaces and the Chern-Ricci flow
• Stability and regularity of solutions of the Monge-Ampère equation on Hermitian manifolds
• The Chern-Ricci flow on Oeljeklaus-Toma manifolds
• Regularizing properties of Complex Monge-Ampère flows II: Hermitian manifolds
• The Chern-Ricci flow and holomorphic bisectional curvature
• The Chern-Ricci flow
• Ricci Curvatures on Hermitian manifolds
• Continuous solutions to Monge-Ampère equations on Hermitian manifolds for measures dominated by capacity
• Long time existence of the (n-1)-plurisubharmonic flow
• Leafwise flat forms on Inoue-Bombieri surfaces
• The Kähler-Ricci flow on compact Kähler manifolds