Determination of the pluripolar hull of graphs of certain holomorphic functions

[Détermination de l'enveloppe pluripolaire des graphes de certaines fonctions holomorphes]

Edigarian, Armen ; Wiegerinck, Jan

Annales de l'Institut Fourier, Tome 54 (2004), p. 2085-2104 / Harvested from Numdam

Résumé

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

Abstract

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

Détail

Publié le : 2004-01-01

MR 2134233 | Zbl 1083.32009

DOI : https://doi.org/10.5802/aif.2075
Classification:  32U30,  30B40,  31B15
Mots clés: fonction plurisousharmonique, enveloppe pluripolaire, ensemble pluricomplète, mesure pluriharmonique, graphe de fonction holomorphe

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