The image of a finely holomorphic map is pluripolar

2007/01/04 by Armen Edigarian, Edigarian, Armen, Said El Marzguioui +3
Mathematics · #31C40 #32U15 #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory #math.CV #msc:31C40 #msc:32U15

paper · pdf · doi:10.48550/arxiv.math/0701136

15 pages, revised version: an example is added, Theorem 1.1 has been generalized to functions of several variables

openalex publication_date 2007/01/04 · arxiv created 2008/01/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the image of a finely holomorphic map on a fine domain in ℂ is pluripolar subset of ℂⁿ. We also discuss the relationship between pluripolar hulls and finely holomorphic function.

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