Regularizing properties of complex Monge–Ampère flows II: Hermitian manifolds

摘要

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.