The complex Monge-Ampere equation on compact Kaehler manifolds

Abstract

We consider the complex Monge-Ampère equation on a compact Kähler manifold $(M,g)$ when the right hand side $F$ has rather weak regularity. In particular we prove that estimate of $\tϕ$ and the gradient estimate hold when $F$ is in $W^{1,p_0}$ for any $p_0>2n$. As an application, we show that there exists a classical solution in $W^{3,p_0}$ for the complex Monge-Ampère equation when $F$ is in $W^{1,p_0}$.

17 pages; references are corrected and added

References in corpus (9)

• The Space of Kähler metrics (II)
• Interior estimates for solutions of Abreu's equation
• Space of Ricci flows (II)
• Singular Kahler-Einstein metrics
• K-stability of constant scalar curvature Kähler manifolds
• Complex Monge-Ampere equations on Hermitian manifolds
• Relative K-stability of extremal metrics
• On Pointwise Gradient Estimates for the Complex Monge-Ampere Equation
• On regularity of complex Monge-Ampere equation

Cited by in corpus (1)

• Conic singularities metrics with prescribed scalar curvature: a priori estimates for normal crossing divisors