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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Graphs that are not complete pluripolar


Authors: Armen Edigarian and Jan Wiegerinck
Journal: Proc. Amer. Math. Soc. 131 (2003), 2459-2465
MSC (2000): Primary 32U30; Secondary 31A15
Published electronically: January 8, 2003
MathSciNet review: 1974644
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Abstract: Let $D_1\subset D_2$ be domains in $ \mathbb{C} $. Under very mild conditions on $D_2$ we show that there exist holomorphic functions $f$, defined on $D_1$with the property that $f$ is nowhere extendible across $\partial D_1$, while the graph of $f$ over $D_1$ is not complete pluripolar in $D_2\times\mathbb{C} $. This refutes a conjecture of Levenberg, Martin and Poletsky (1992).


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Additional Information

Armen Edigarian
Affiliation: Institute of Mathematics, Jagiellonian University, Reymonta 4/526, 30-059 Kraków, Poland
Email: edigaria@im.uj.edu.pl

Jan Wiegerinck
Affiliation: Faculty of Mathematics, University of Amsterdam, Plantage Muidergracht 24, 1018 TV, Amsterdam, The Netherlands
Email: janwieg@science.uva.nl

DOI: http://dx.doi.org/10.1090/S0002-9939-03-06947-8
PII: S 0002-9939(03)06947-8
Keywords: Plurisubharmonic function, pluripolar hull, complete pluripolar set, harmonic measure
Received by editor(s): March 15, 2002
Published electronically: January 8, 2003
Additional Notes: The first author was supported in part by KBN grant No. 5 P03A 033 21. The first author is a fellow of the A. Krzyżanowski Foundation (Jagiellonian University)
Communicated by: Mei-Chi Shaw
Article copyright: © Copyright 2003 American Mathematical Society