Complex Monge-Ampere equations on Hermitian manifolds

2009/06/18 by Bo Guan, Qun Li, Guan, Bo +1 · 3 citations
Mathematics · #32W20 #35J25 #53C55 #58J05 #58J32 #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.CV #math.DG #msc:32W20 #msc:35J25 #msc:53C55 #msc:58J05 #msc:58J32

paper · pdf · doi:10.48550/arxiv.0906.3548

arxiv created 2009/06/18 · openalex publication_date 2009/06/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study complex Monge-Ampere equations on Hermitian manifolds, extending classical existence results of Yau and Aubin in the Kahler case, and those of Caffarelli, Kohn, Nirenberg and Spruck for the Dirichlet problem in Cⁿ. As an application we generalize existing results on the Donaldson conjecture on geodesics in the space of Kahler metrics to the Hermitian setting.

Cited by

• The complex Monge-Ampère equation on some compact Hermitian manifolds
• The Dirichlet Problem of Fully Nonlinear Equations on Hermitian\n Manifolds
• Regularity of A Complex Monge-Ampère Equation on Hermitian Manifolds

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