Monge-Ampère equations with prescribed singularities on compact Hermitian manifolds

2025/11/04 by Alehyane, Omar, Lu, Chinh H., Salouf, Mohammed
Mathematics · #32Q15 #32U05 #32W20 #35A23 #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · doi:10.48550/arxiv.2511.02339

openalex publication_date 2025/11/04 · openalex created_date 2025/11/06 · openalex updated_date 2026/07/28

Abstract

Given a compact complex manifold X, we study the existence and the uniqueness of weak solutions to degenerate Monge-Ampère equations on X with prescribed singularities when the reference form is semipositive and big, while the right hand side is a non-pluripolar positive Radon measure. This generalizes our previous work to more general hermitian manifolds and also to the case of solutions with prescribed singularities.

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Related

• Degenerate complex Monge-Ampère equations on some compact Hermitian manifolds
• Weak solutions to Monge-Ampère type equations on compact Hermitian manifold with boundary
• Degenerate complex Monge-Amp\` ere type equations on compact Hermitian manifolds and applications
• Degenerate complex Monge-Ampère type equations on compact Hermitian manifolds and applications II
• Monge-Ampère type equation on compact Hermitian manifolds