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Regularizing properties of Complex Monge-Ampère flows II: Hermitian manifolds (1701.04023v3)
Published 15 Jan 2017 in math.CV, math.AP, and math.DG
Abstract: We prove that a general complex Monge-Amp`ere 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.