A note on equality on plurifinely open sets of some complex Monge-Ampère measures

2023/10/16 by Mohamed El Kadiri, Kadiri, Mohamed El
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.2310.10367

openalex publication_date 2023/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Our aim in this paper is to prove that if plurisubharmonic functions u₁,. . . , u_n, v₁,. . ., v_n in the domain of definition of the complex Monge-Ampère operator on a domain set D⊂ ℂⁿ (n≥ 1) are such that u₁= v₁, . . ., u_n=v_n on a Borel plurifinely open set Ω⊂ D, then dd^cu₁\wedge ...\wedge dd^cu_n=dd^cv₁\wedge ...\wedge dd^cv_n on Ω. This extends an earlier result obtained by the author in \citeEK.

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