Graphs that are not complete pluripolar

2002/03/07 by Armen Edigarian, Edigarian, Armen, Jan Wiegerinck +1
Mathematics · #31A15 #32U30 #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.CV #msc:31A15 #msc:32U30

paper · pdf · doi:10.48550/arxiv.math/0203064

7 pages

arxiv created 2002/03/07 · openalex publication_date 2002/03/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let D₁ be a subdomain of D₂ in the complex plane CC. Under very mild conditions on D₂ we show that there exist holomorphic functions f, defined on D₁ with the property that f is nowhere extendible across the boundary of D₁, while the graph of f over D₁ is NOT complete pluripolar in D₂ times CC. This refutes a conjecture of Levenberg, Martin and Poletsky.

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