The complex monge-ampère equation on some compact hermitian manifolds

Jianchun Chu

doi:10.2140/pjm.2015.276.369

The complex monge-ampère equation on some compact hermitian manifolds

Jianchun Chu^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We consider the complex Monge-Ampère equation on compact manifolds when the background metric is a Hermitian metric (in complex dimension 2) or a Hermitian metric satisfying an additional condition (in higher dimensions). We prove that the Laplacian estimate holds when F is in W^1,q0 for any q0 > 2n. As an application, we show that, up to scaling, there exists a unique classical solution in W^3,q0 for the complex Monge-Ampère equation when F is in W^1,q0.

Original language	English (US)
Pages (from-to)	369-386
Number of pages	18
Journal	Pacific Journal of Mathematics
Volume	276
Issue number	2
DOIs	https://doi.org/10.2140/pjm.2015.276.369
State	Published - 2015

Keywords

Compact hermitian manifold
Complex monge-ampère equation

ASJC Scopus subject areas

Mathematics(all)

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abstract = "We consider the complex Monge-Amp{\`e}re equation on compact manifolds when the background metric is a Hermitian metric (in complex dimension 2) or a Hermitian metric satisfying an additional condition (in higher dimensions). We prove that the Laplacian estimate holds when F is in W1,q0 for any q0 > 2n. As an application, we show that, up to scaling, there exists a unique classical solution in W3,q0 for the complex Monge-Amp{\`e}re equation when F is in W1,q0.",

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