no. 6
Determination of the pluripolar hull of graphs of certain holomorphic functions
[Détermination de l'enveloppe pluripolaire des graphes de certaines fonctions holomorphes]
Edigarian, Armen1 ; 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.

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×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.

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

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) 
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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. https://aif.centre-mersenne.org/articles/10.5802/aif.2075/

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