On the modulus of continuity of solutions to complex Monge-Ampère equations

2021/12/04 by Guo, Bin, Phong, Duong H., Tong, Freid +1 · 4 citations
#Analysis of PDEs (math.AP) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2112.02354

Abstract

In this paper, we prove a uniform and sharp estimate for the modulus of continuity of solutions to complex Monge-Ampère equations, using the PDE-based approach developed by the first three authors in their approach to supremum estimates for fully non-linear equations in Kähler geometry. As an application, we derive a uniform diameter bound for Kähler metrics satisfying certain Monge-Ampère equations.

Cited by

• Kähler-Ricci flows coming out of metric spaces
• Modulus of continuity for solutions to complex Monge-Ampère equations on Hermitian manifolds
• Continuity of solutions to complex Hessian equations on compact Hermitian manifolds
• Hölder estimates for degenerate complex Monge-Ampère equations

Related

• Modulus of continuity for solutions to complex Monge-Ampère equations on Hermitian manifolds
• Geometric estimates for complex Monge-Ampere equations
• Modulus of continuity of Monge--Ampère potentials in big cohomology classes
• Uniform estimates: from Yau to Kolodziej
• Modulus of Continuity of Solutions to Complex Monge-Ampère Equations on Stein Spaces