Regularizing properties of Complex Monge-Ampère flows

Abstract

We study the regularizing properties of complex Monge-Ampère flows on a Kähler manifold $(X,\omega )$ when the initial data are $\omega$-psh functions with zero Lelong number at all points. We prove that the general Monge-Ampère flow has a solution which is immediately smooth. We also prove the uniqueness and stability of solution.

30 pages

References in corpus (1)

• The Kahler-Ricci flow through singularities

Cited by in corpus (3)

• Regularizing properties of Complex Monge-Ampère flows II: Hermitian manifolds
• Pluripotential kahler-ricci flows
• Singularities of the Chern-Ricci flow