Pluripotential estimates on compact Hermitian manifolds

Abstract

We discuss pluripotential aspects of the Monge-Ampère equations on compact Hermitian manifolds and prove $L^{\infty }$ estimates for any metric, as well as the existence of weak solutions under an extra assumption.

14 pages; preliminary version

References in corpus (1)

• An Inequality for Mixed Monge-Ampère measures

Cited by in corpus (11)

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• Weak solutions of complex Hessian equations on compact Hermitian manifolds
• Stability and regularity of solutions of the Monge-Ampère equation on Hermitian manifolds
• Weak transcendental holomorphic Morse inequalities on compact Kähler manifolds
• Regularizing properties of Complex Monge-Ampère flows II: Hermitian manifolds
• Plurisubharmonic functions and nef classes on complex manifolds
• On Pointwise Gradient Estimates for the Complex Monge-Ampere Equation
• Regularity of A Complex Monge-Ampère Equation on Hermitian Manifolds
• Hölder continuous solutions of the Monge-Ampère equation on compact Hermitian manifolds
• The Dirichlet problem for a complex Hessian equation on compact Hermitian manifolds with boundary
• Some interior regularity estimates for solutions of complex Monge-Ampère equations on a ball