The complex Monge-Ampère equation on some compact Hermitian manifolds

Jianchun Chu

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arXiv · 1404.5445

The complex Monge-Ampère equation on some compact Hermitian manifolds

Jianchun Chu

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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 $W^{1,q_{0}}$.

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BibTeX RIS

Jianchun Chu. 2014-05-15. The complex Monge-Ampère equation on some compact Hermitian manifolds. https://arxiv.org/abs/1404.5445

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