Geometric estimates for complex Monge-Ampere equations

Abstract

We prove uniform gradient and diameter estimates for a family of geometric complex Monge-Ampere equations. Such estimates can be applied to study geometric regularity of singular solutions of complex Monge-Ampere equations. We also prove a uniform diameter estimate for collapsing families of twisted Kahler-Einstein metrics on Kahler manifolds of nonnegative Kodaira dimensions.

References in corpus (9)

• The Kähler-Ricci flow, Ricci-flat metrics and collapsing limits
• Riemannian geometry of Kahler-Einstein currents
• Singular Kahler-Einstein metrics
• Interior derivative estimates for the Kähler-Ricci flow
• Ricci flow and birational surgery
• Degeneration of Kahler-Einstein manifolds of negative scalar curvature
• Riemannian geometry of Kahler-Einstein currents II: an analytic proof of Kawamata's base point free theorem
• Bounding diameter of singular Kähler metric
• The continuity method on minimal elliptic Kähler surfaces

Cited by in corpus (3)

• Collapsing behavior of Ricci-flat Kahler metrics and long time solutions of the Kahler-Ricci flow
• Riemannian geometry of Kahler-Einstein currents III: compactness of Kahler-Einstein manifolds of negative scalar curvature
• Kahler-Ricci flow on blowups along submanifolds