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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Relative extremal functions and characterization of pluripolar sets in complex manifolds


Authors: Armen Edigarian and Ragnar Sigurdsson
Journal: Trans. Amer. Math. Soc. 362 (2010), 5321-5331
MSC (2010): Primary 32U15; Secondary 32U20, 32E20
DOI: https://doi.org/10.1090/S0002-9947-2010-05080-9
Published electronically: May 20, 2010
MathSciNet review: 2657681
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Abstract: We study a disc formula for the relative extremal function for a subset of a complex manifold and apply it to give a description of pluripolar sets and polynomial hulls.


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Additional Information

Armen Edigarian
Affiliation: Institute of Mathematics, Jagiellonian University, Lojasiewicza 6, 30-348 Kraków, Poland
Email: Armen.Edigarian@im.uj.edu.pl

Ragnar Sigurdsson
Affiliation: Science Institute, University of Iceland, Dunhaga 3, IS-107 Reykjavik, Iceland
Email: ragnar@hi.is

DOI: https://doi.org/10.1090/S0002-9947-2010-05080-9
Keywords: Analytic disc, relative extremal function, pluriregular set, pluripolar set, Josefson manifold
Received by editor(s): June 28, 2008
Published electronically: May 20, 2010
Additional Notes: This work was a part of the Research Grant No. 1 PO3A 005 28, which was supported by public means in the programme for promoting science in Poland in the years 2005-2008. The first author was a fellow of Krzyżanowski Fund at the Jagiellonian University. This work was supported by the Research Fund at the University of Iceland.
Article copyright: © Copyright 2010 American Mathematical Society