Weak convergence of Monge-Ampère measures on compact Hermitian manifolds

2022/12/22 by Sławomir Kołodziej, Ngoc Cuong Nguyen, Kolodziej, Slawomir +1 · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2212.11550

openalex publication_date 2022/12/22 · openalex created_date 2023/02/15 · openalex updated_date 2026/07/28

Abstract

We give a sufficient condition on a sequence of uniformly bounded ω-plurisubharmonic functions, ω being a Hermitian metric, for which the sequence of associated Monge-Ampère measures converges weakly. This criterion can be used to obtained a bounded ω-plurisubharmonic solution to the Monge-Ampère equation.

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• Mixed Hessian inequalities on Hermitian manifolds and applications

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