Determination of the pluripolar hull of graphs of certain holomorphic functions

Armen Edigarian[1]; Jan Wiegerinck

  • [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 (2004)

  • Volume: 54, Issue: 6, page 2085-2104
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Edigarian, Armen, and Wiegerinck, Jan. "Determination of the pluripolar hull of graphs of certain holomorphic functions." Annales de l’institut Fourier 54.6 (2004): 2085-2104. <http://eudml.org/doc/116168>.

@article{Edigarian2004,
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.},
affiliation = {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)},
author = {Edigarian, Armen, Wiegerinck, Jan},
journal = {Annales de l’institut Fourier},
keywords = {Plurisubharmonic function; pluripolar hull; complete pluripolar set; pluriharmonic measure; graph of holomorphic function; plurisubharmonic function},
language = {eng},
number = {6},
pages = {2085-2104},
publisher = {Association des Annales de l'Institut Fourier},
title = {Determination of the pluripolar hull of graphs of certain holomorphic functions},
url = {http://eudml.org/doc/116168},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Edigarian, Armen
AU - Wiegerinck, Jan
TI - Determination of the pluripolar hull of graphs of certain holomorphic functions
JO - Annales de l’institut Fourier
PY - 2004
PB - Association des Annales de l'Institut Fourier
VL - 54
IS - 6
SP - 2085
EP - 2104
AB - 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.
LA - eng
KW - Plurisubharmonic function; pluripolar hull; complete pluripolar set; pluriharmonic measure; graph of holomorphic function; plurisubharmonic function
UR - http://eudml.org/doc/116168
ER -

References

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