Complex Monge-Ampere equations on Hermitian manifolds

Abstract

We study complex Monge-Ampere equations on Hermitian manifolds, extending classical existence results of Yau and Aubin in the Kahler case, and those of Caffarelli, Kohn, Nirenberg and Spruck for the Dirichlet problem in $C^n$. As an application we generalize existing results on the Donaldson conjecture on geodesics in the space of Kahler metrics to the Hermitian setting.

References in corpus (1)

• The Space of Kähler metrics (II)

Cited by in corpus (9)

• Regularity results for pluriclosed flow
• The Dirichlet Problem of Fully Nonlinear Equations on Hermitian Manifolds
• On Pointwise Gradient Estimates for the Complex Monge-Ampere Equation
• Regularity estimates of solutions to complex Monge-Ampère equations on Hermitian manifolds
• Deformed Hermitian-Yang-Mills Equation on Compact Hermitian Manifolds
• Regularity of A Complex Monge-Ampère Equation on Hermitian Manifolds
• Parabolic complex Monge-Ampère equations on compact Hermitian manifolds
• The complex Monge-Ampere equation on compact Kaehler manifolds
• The complex Monge-Ampère equation on some compact Hermitian manifolds