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

 

On the Hartogs-Bochner phenomenon for CR functions in $P_2(\mathbb{C})$


Authors: Roman Dwilewicz and Joël Merker
Journal: Proc. Amer. Math. Soc. 130 (2002), 1975-1980
MSC (2000): Primary 32V25; Secondary 32V10, 32V15, 32D15
Published electronically: February 27, 2002
MathSciNet review: 1896029
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Abstract: Let $M$ be a compact, connected, $\mathcal{C}^2$-smooth and globally minimal hypersurface $M$ in $P_2(\mathbb{C})$ which divides the projective space into two connected parts $U^{+}$ and $U^{-}$. We prove that there exists a side, $U^-$ or $U^+$, such that every continuous CR function on $M$ extends holomorphically to this side. Our proof of this theorem is a simplification of a result originally due to F. Sarkis.


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Additional Information

Roman Dwilewicz
Affiliation: Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, P.O. Box 137, 00-950 Warsaw, Poland
Email: rd@impan.gov.pl

Joël Merker
Affiliation: Laboratoire d’Analyse, Topologie et Probabilités, Centre de Mathématiques et Informatique, UMR 6632, 39 rue Joliot Curie, F-13453 Marseille Cedex 13, France
Email: merker@cmi.univ-mrs.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06357-8
PII: S 0002-9939(02)06357-8
Keywords: Smooth hypersurfaces of the complex projective space, holomorphic extension of CR functions, jump formula, global minimality, one-sided neighborhood
Received by editor(s): December 13, 2000
Published electronically: February 27, 2002
Additional Notes: This research was partially supported by a grant of the Polish Committee for Scientific Research KBN 2 PO3A 044 15 and by a grant from the French-Polish program “Polonium 1999”
Communicated by: Steven R. Bell
Article copyright: © Copyright 2002 American Mathematical Society