Stability and regularity of solutions of the Monge-Ampère equation on Hermitian manifolds

Abstract

We prove stability of solutions of the complex Monge-Ampère equation on compact Hermitian manifolds, when the right hand side varies in a bounded set in $L^p,p>1$ and it is bounded away from zero. Such solutions are shown to be Hölder continuous. As an application we extend a recent result of Székelyhidi and Tosatti on Kähler-Einstein equation from Kähler to Hermitian manifolds.

v4 final version incorporated the referee report

References in corpus (4)

• The Kähler-Ricci flow on surfaces of positive Kodaira dimension
• Pluripotential estimates on compact Hermitian manifolds
• Form-type Calabi-Yau equations on Kähler manifolds of nonnegative orthogonal bisectional curvature
• An Inequality for Mixed Monge-Ampère measures

Cited by in corpus (3)

• Weak Solutions of the Chern-Ricci flow on compact complex surfaces
• Leafwise flat forms on Inoue-Bombieri surfaces
• Hölder continuous solutions of the Monge-Ampère equation on compact Hermitian manifolds