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Izv. Akad. Nauk SSSR Ser. Mat., 1982, Volume 46, Issue 1, Pages 28–35 (Mi izv1603)  

This article is cited in 7 scientific papers (total in 8 papers)

Holomorphic extension of mappings of compact hypersurfaces

A. G. Vitushkin


Abstract: In this article it is proved that any holomorphic mapping of a compact, nonspherical, strictly pseudoconvex real-analytic hypersurface in an $n$-dimensional complex manifold ($n\geqslant2$) onto another such surface extends holomorphically to a neighborhood of the first surface which is independent of the choice of mapping, and that the family of extensions of mappings is equicontinuous in this neighborhood.
Bibliography: 4 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1983, 20:1, 27–33

Bibliographic databases:

UDC: 517.5
MSC: Primary 32D15; Secondary 32H99, 32C05
Received: 18.09.1981

Citation: A. G. Vitushkin, “Holomorphic extension of mappings of compact hypersurfaces”, Izv. Akad. Nauk SSSR Ser. Mat., 46:1 (1982), 28–35; Math. USSR-Izv., 20:1 (1983), 27–33

Citation in format AMSBIB
\Bibitem{Vit82}
\by A.~G.~Vitushkin
\paper Holomorphic extension of mappings of compact hypersurfaces
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1982
\vol 46
\issue 1
\pages 28--35
\mathnet{http://mi.mathnet.ru/izv1603}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=643891}
\zmath{https://zbmath.org/?q=an:0571.32011}
\transl
\jour Math. USSR-Izv.
\yr 1983
\vol 20
\issue 1
\pages 27--33
\crossref{https://doi.org/10.1070/IM1983v020n01ABEH001337}


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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. A. V. Loboda, “Linearizability of automorphisms of non-spherical surfaces”, Math. USSR-Izv., 21:1 (1983), 171–186  mathnet  crossref  mathscinet  zmath
    2. S. M. Ivashkovich, “Extension of locally biholomorphic mappings of domains into complex projective space”, Math. USSR-Izv., 22:1 (1984), 181–189  mathnet  crossref  mathscinet  zmath
    3. A. G. Vitushkin, “Real-analytic hypersurfaces in complex manifolds”, Russian Math. Surveys, 40:2 (1985), 1–35  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. A. G. Vitushkin, “Extension of the germ of a holomorphic map of a strictly pseudo-convex surface”, Russian Math. Surveys, 40:4 (1985), 229–230  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. N. G. Kruzhilin, “Local automorphisms and mappings of smooth strictly pseudoconvex hypersurfaces”, Math. USSR-Izv., 26:3 (1986), 531–552  mathnet  crossref  mathscinet  zmath  isi
    6. V. V. Ezhov, “Linearization of stability groups of a class of hypersurfaces”, Russian Math. Surveys, 41:3 (1986), 203–204  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. V. K. Beloshapka, V. S. Vladimirov, A. A. Gonchar, E. P. Dolzhenko, N. G. Kruzhilin, V. V. Napalkov, P. V. Paramonov, A. G. Sergeev, P. L. Ul'yanov, E. M. Chirka, “Anatolii Georgievich Vitushkin (on his 70th birthday)”, Russian Math. Surveys, 57:1 (2002), 183–190  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    8. Michael Eastwood, Alexander Isaev, “Examples of unbounded homogeneous domains in complex space”, Sci China Ser A, 48:s1 (2005), 248  crossref  mathscinet  zmath
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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