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

This article is cited in 4 scientific papers (total in 4 papers)

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.

Full text: PDF file (2110 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1982, 19:1, 171–188

Bibliographic databases:

UDC: 517.5
MSC: 32F99
Received: 10.03.1981

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  mathnet  crossref  mathscinet  zmath
    2. N. G. Kruzhilin, “Foliations connected with the Monge–Ampère equation in Hartogs domains”, Math. USSR-Izv., 25:2 (1985), 419–427  mathnet  crossref  mathscinet  zmath  isi
    3. R. A. Airapetyan, “Extension of CR-functions from piecewise smooth CR-manifolds”, Math. USSR-Sb., 62:1 (1989), 111–120  mathnet  crossref  mathscinet  zmath
    4. E. M. Chirka, “Introduction to the geometry of $CR$-manifolds”, Russian Math. Surveys, 46:1 (1991), 95–197  mathnet  crossref  mathscinet  zmath  adsnasa  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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