Determination of the pluripolar hull of graphs of certain holomorphic functions

Edigarian, Armen; Wiegerinck, Jan

doi:10.5802/aif.2075

Determination of the pluripolar hull of graphs of certain holomorphic functions
[Détermination de l'enveloppe pluripolaire des graphes de certaines fonctions holomorphes]

Edigarian, Armen ¹ ; Wiegerinck, Jan

¹ Jagiellonian University, Institute of Mathematics, Reymonta 4/526, 30-059 Kraków (Poland), University of Amsterdam, Faculty of Mathematics, Plantage Muidergracht 24, 1018 TV, Amsterdam (The Netherlands)

Annales de l'Institut Fourier, Tome 54 (2004) no. 6, pp. 2085-2104.

Résumé
Abstract

Soit $A$ sous-ensemble fermé polaire d’un domaine $D$ de $ℂ$ . On donne une description complète de l’enveloppe pluripolaire du graphe $Γ$ d’une fonction holomorphe définie sur $D ∖ A$ . Pour achever ce résultat on prouve des propriétés de semi-continuité et un principe de localisation de mesure pluriharmonique.

Let $A$ be a closed polar subset of a domain $D$ in $ℂ$ . We give a complete description of the pluripolar hull $Γ_{D \times ℂ}^{*}$ of the graph $Γ$ of a holomorphic function defined on $D ∖ A$ . To achieve this, we prove for pluriharmonic measure certain semi-continuity properties and a localization principle.

MR Zbl

DOI : 10.5802/aif.2075

Classification : 32U30, 30B40, 31B15
Keywords: Plurisubharmonic function, pluripolar hull, complete pluripolar set, pluriharmonic measure, graph of holomorphic function
Mot clés : fonction plurisousharmonique, enveloppe pluripolaire, ensemble pluricomplète, mesure pluriharmonique, graphe de fonction holomorphe

Affiliations des auteurs :

Edigarian, Armen ¹ ; Wiegerinck, Jan

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     title = {Determination of the pluripolar hull of graphs of certain holomorphic functions},
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     pages = {2085--2104},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
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Edigarian, Armen; Wiegerinck, Jan. Determination of the pluripolar hull of graphs of certain holomorphic functions. Annales de l'Institut Fourier, Tome 54 (2004) no. 6, pp. 2085-2104. doi : 10.5802/aif.2075. http://www.numdam.org/articles/10.5802/aif.2075/

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