Fibrations and Stein neighborhoods
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- by Franc Forstnerič and Erlend Fornæss Wold PDF
- Proc. Amer. Math. Soc. 138 (2010), 2037-2042 Request permission
Abstract:
Let $Z$ be a complex space and let $S$ be a compact set in $\mathbb {C}^n \times Z$ which is fibered over $\mathbb {R}^n$. We give a necessary and sufficient condition for $S$ to be a Stein compactum.References
- Eric Bedford and John Erik Fornaess, Domains with pseudoconvex neighborhood systems, Invent. Math. 47 (1978), no. 1, 1–27. MR 499316, DOI 10.1007/BF01609476
- Mihnea Colţoiu, Complete locally pluripolar sets, J. Reine Angew. Math. 412 (1990), 108–112. MR 1074376, DOI 10.1515/crll.1990.412.108
- Jean-Pierre Demailly, Cohomology of $q$-convex spaces in top degrees, Math. Z. 204 (1990), no. 2, 283–295. MR 1055992, DOI 10.1007/BF02570874
- Klas Diederich and John Erik Fornaess, Pseudoconvex domains: an example with nontrivial Nebenhülle, Math. Ann. 225 (1977), no. 3, 275–292. MR 430315, DOI 10.1007/BF01425243
- Franc Forstneric, Interpolation by holomorphic automorphisms and embeddings in $\textbf {C}^n$, J. Geom. Anal. 9 (1999), no. 1, 93–117. MR 1760722, DOI 10.1007/BF02923090
- Franc Forstnerič, Extending holomorphic mappings from subvarieties in Stein manifolds, Ann. Inst. Fourier (Grenoble) 55 (2005), no. 3, 733–751 (English, with English and French summaries). MR 2149401
- Forstnerič, F., The Oka principle for sections of stratified fiber bundles. Pure Appl. Math. Quarterly (special issue in honor of Joseph J. Kohn), 6 (2010), no. 3, 843–874.
- Forstnerič, F., Oka manifolds. C. R. Acad. Sci. Paris, Ser. I, 347 (2009), 1017–1020.
- Franc Forstnerič and Christine Laurent-Thiébaut, Stein compacts in Levi-flat hypersurfaces, Trans. Amer. Math. Soc. 360 (2008), no. 1, 307–329. MR 2342004, DOI 10.1090/S0002-9947-07-04263-8
- Robert C. Gunning and Hugo Rossi, Analytic functions of several complex variables, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1965. MR 0180696
- Lars Hörmander, An introduction to complex analysis in several variables, 3rd ed., North-Holland Mathematical Library, vol. 7, North-Holland Publishing Co., Amsterdam, 1990. MR 1045639
- Manne, P. E., Wold, E. F., Øvrelid, N., Carleman approximation by entire functions on Stein manifolds. Preprint, University of Oslo (2008).
- Raghavan Narasimhan, The Levi problem for complex spaces, Math. Ann. 142 (1960/61), 355–365. MR 148943, DOI 10.1007/BF01451029
- Stephen Scheinberg, Uniform approximation by entire functions, J. Analyse Math. 29 (1976), 16–18. MR 508100, DOI 10.1007/BF02789974
- Yum Tong Siu, Every Stein subvariety admits a Stein neighborhood, Invent. Math. 38 (1976/77), no. 1, 89–100. MR 435447, DOI 10.1007/BF01390170
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
- Erlend Fornæss Wold
- Affiliation: Matematisk Institutt, Universitetet i Oslo, Postboks 1053 Blindern, 0316 Oslo, Norway
- MR Author ID: 757618
- Email: erlendfw@math.uio.no
- Received by editor(s): June 12, 2009
- Received by editor(s) in revised form: September 12, 2009
- Published electronically: December 8, 2009
- Additional Notes: The first author was supported by grants P1-0291 and J1-6173, Republic of Slovenia.
- Communicated by: Mei-Chi Shaw
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 2037-2042
- MSC (2010): Primary 32E05, 32E10, 32H02, 32V40
- DOI: https://doi.org/10.1090/S0002-9939-09-10223-X
- MathSciNet review: 2596039