Extremal omega-plurisubharmonic functions as envelopes of disc functionals - Generalization and applications to the local theory

2011/03/22 by Benedikt Steinar Magnússon, Benedikt Steinar Magnusson, Magnusson, Benedikt Steinar
Mathematics · #32U05 #32U40 #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory #math.CV #msc:32U05 #msc:32U40

paper · pdf · doi:10.48550/arxiv.1103.4297

24 pages; minor corrections and notation for the extension over sing(ω) clarified

openalex publication_date 2011/03/22 · arxiv created 2011/07/19 · arxiv updated 2011/07/20 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

We generalize the Poletsky disc envelope formula for the function sup \u ∈ \PSH(X,ω) ; u≤ ϕ\ on any complex manifold X to the case where the real (1,1)-current ω=ω₁-ω₂ is the difference of two positive closed (1,1)-currents and ϕ is the difference of an ω₁-upper semicontinuous function and a plurisubharmonic function.

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