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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Stein compacts in Levi-flat hypersurfaces


Authors: Franc Forstneric and Christine Laurent-Thiébaut
Journal: Trans. Amer. Math. Soc. 360 (2008), 307-329
MSC (2000): Primary 32D15, 32T20, 32T27, 32V05, 32V25; Secondary 57R30
Published electronically: July 23, 2007
MathSciNet review: 2342004
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Abstract: We explore connections between geometric properties of the Levi foliation of a Levi-flat hypersurface $ M$ and holomorphic convexity of compact sets in $ M$, or bounded in part by $ M$. Applications include extendability of Cauchy-Riemann functions, solvability of the $ \overline{\partial}_b$-equation, approximation of Cauchy-Riemann and holomorphic functions, and global regularity of the $ \overline{\partial}$-Neumann operator.


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Additional Information

Franc Forstneric
Affiliation: Institute of Mathematics, Physics and Mechanics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia
Email: franc.forstneric@fmf.uni-lj.si

Christine Laurent-Thiébaut
Affiliation: Institut Fourier, UMR 5582 CNRS/UJF, BP 74, 38402 St. Martin d’Hères Cedex, France
Email: Christine.Laurent@ujf-grenoble.fr

DOI: http://dx.doi.org/10.1090/S0002-9947-07-04263-8
PII: S 0002-9947(07)04263-8
Keywords: Levi-flat hypersurfaces, foliations, Stein manifolds
Received by editor(s): March 17, 2005
Received by editor(s) in revised form: February 7, 2006
Published electronically: July 23, 2007
Additional Notes: The first author was supported by grants P1-0291 and J1-6173, Republic of Slovenia.
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.