The Dirichlet problem for Monge-Ampère equation for (n-1)-PSH functions on Hermitian manifolds

2022/03/14 by Rirong Yuan, Yuan, Rirong
Mathematics · #Algebraic Geometry and Number Theory #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2203.07232

openalex publication_date 2022/03/14 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

Abstract

We solve the Dirichlet problem for Monge-Ampère equation for (n-1)-PSH functions possibly with degenerate right-hand side, through deriving a quantitative version of boundary estimate under the assumption of (n-1)-PSH subsolutions. In addition, we confirm the subsolution assumption on a product of a closed balanced manifold with a compact Riemann surface with boundary.

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