Regularizing properties of Complex Monge-Ampère flows II: Hermitian manifolds

Abstract

We prove that a general complex Monge-Ampère flow on a Hermitian manifold can be run from an arbitrary initial condition with zero Lelong number at all points. Using this property, we confirm a conjecture of Tosatti-Weinkove: the Chern-Ricci flow performs a canonical surgical contraction. Finally, we study a generalization of the Chern-Ricci flow on compact Hermitian manifolds, namely the twisted Chern-Ricci flow.

32 pages, final version, to appear in Math. Ann

References in corpus (5)

• Pluripotential estimates on compact Hermitian manifolds
• The Anomaly flow and the Fu-Yau equation
• Regularizing properties of Complex Monge-Ampère flows
• Anomaly flows
• Weak Solutions of the Chern-Ricci flow on compact complex surfaces

Cited by in corpus (6)

• The Chern-Ricci flow
• Instantaneously complete Chern-Ricci flow and Kähler-Einstein metrics
• Continuous solutions to Monge-Ampère equations on Hermitian manifolds for measures dominated by capacity
• Weak Solutions of the Chern-Ricci flow on compact complex surfaces
• Leafwise flat forms on Inoue-Bombieri surfaces
• Singularities of the Chern-Ricci flow