Stein compacts in Levi-flat hypersurfaces
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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.References
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Additional Information
- Franc Forstnerič
- Affiliation: Institute of Mathematics, Physics and Mechanics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia
- MR Author ID: 228404
- 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
- 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.
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 360 (2008), 307-329
- MSC (2000): Primary 32D15, 32T20, 32T27, 32V05, 32V25; Secondary 57R30
- DOI: https://doi.org/10.1090/S0002-9947-07-04263-8
- MathSciNet review: 2342004