The complex Monge-Ampère equation on some compact Hermitian manifolds

2014/04/22 by Jianchun Chu, Chu, Jianchun
Mathematics · #Algebraic Geometry and Number Theory #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1404.5445

openalex publication_date 2014/04/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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,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.

Citations

• Complex Monge-Ampere equations on Hermitian manifolds

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