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 Izv. Akad. Nauk SSSR Ser. Mat., 1981, Volume 45, Issue 4, Pages 874–895 (Mi izv1589)

The Levi form for $C^1$-smooth hypersurfaces, and the complex structure on the boundary of domains of holomorphy

N. V. Shcherbina

Abstract: A description is given of the set of those boundary points of a domain of holomorphy $D\subset\mathbf C^2$ which have a neighborhood in which the boundary fibers into analytic curves. For domains with $C^1$-smooth boundary whose closure has a basis of Stein neighborhoods this set coincides with the complement of the Shilov boundary $S_{A(\overline D)}$.
Bibliography: 5 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1982, 19:1, 171–188

Bibliographic databases:

UDC: 517.5
MSC: 32F99

Citation: N. V. Shcherbina, “The Levi form for $C^1$-smooth hypersurfaces, and the complex structure on the boundary of domains of holomorphy”, Izv. Akad. Nauk SSSR Ser. Mat., 45:4 (1981), 874–895; Math. USSR-Izv., 19:1 (1982), 171–188

Citation in format AMSBIB
\Bibitem{Shc81} \by N.~V.~Shcherbina \paper The Levi form for $C^1$-smooth hypersurfaces, and the complex structure on the boundary of domains of holomorphy \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1981 \vol 45 \issue 4 \pages 874--895 \mathnet{http://mi.mathnet.ru/izv1589} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=631442} \zmath{https://zbmath.org/?q=an:0513.32019|0487.32009} \transl \jour Math. USSR-Izv. \yr 1982 \vol 19 \issue 1 \pages 171--188 \crossref{https://doi.org/10.1070/IM1982v019n01ABEH001406} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. N. V. Shcherbina, “On fibering into analytic curves of the common boundary of two domains of holomorphy”, Math. USSR-Izv., 21:2 (1983), 399–413
2. N. G. Kruzhilin, “Foliations connected with the Monge–Ampère equation in Hartogs domains”, Math. USSR-Izv., 25:2 (1985), 419–427
3. R. A. Airapetyan, “Extension of CR-functions from piecewise smooth CR-manifolds”, Math. USSR-Sb., 62:1 (1989), 111–120
4. E. M. Chirka, “Introduction to the geometry of $CR$-manifolds”, Russian Math. Surveys, 46:1 (1991), 95–197
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