Singularities of the Chern-Ricci flow

Abstract

We study the nature of finite-time singularities for the Chern-Ricci flow, partially answering a question of Tosatti-Weinkove. We show that a solution of degenerate parabolic complex Monge-Ampère equations starting from arbitrarily positive (1,1)-currents are smooth outside some analytic subset, generalizing works by Di Nezza-Lu. We extend Guedj-Lu's recent approach to establish uniform a priori estimates for degenerate complex Monge-Ampère equations on compact Hermitian manifolds. We apply it to studying the Chern-Ricci flows on complex log terminal varieties starting from an arbitrary current.

arXiv commentfinal version, to appear in Analysis & PDE

References in corpus (9)

• The complex Monge-Ampère equation on compact Hermitian manifolds
• Kähler currents and null loci
• The Chern-Ricci flow on complex surfaces
• Regularizing properties of Complex Monge-Ampère flows II: Hermitian manifolds
• Pluripotential kahler-ricci flows
• The Calabi-Yau Theorem and Kähler currents
• Regularizing properties of Complex Monge-Ampère flows
• Demailly-Lelong numbers on complex spaces
• Pluripotential Chern-Ricci Flows