The complex Monge-Ampère equation on some compact Hermitian manifolds

Abstract

We consider the complex Monge-Ampère equation on compact manifolds when the background metric is a Hermitian metric (in complex dimension two) or a kind of Hermitian metric (in higher dimensions). We prove that the Laplacian estimate holds when $F$ is in $W^{1,q_0}$ for any $q_0>2n$. As an application, we show that, up to scaling, there exists a unique classical solution in $W^{3,q_0}$ for the complex Monge-Ampère equation when $F$ is in $W^{1,q_0}$.

16 pages; main result improved

References in corpus (1)

• Complex Monge-Ampere equations on Hermitian manifolds