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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.
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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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This publication is cited in the following articles:
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A. V. Loboda, “Linearizability of automorphisms of non-spherical surfaces”, Math. USSR-Izv., 21:1 (1983), 171–186
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S. M. Ivashkovich, “Extension of locally biholomorphic mappings of domains into complex projective space”, Math. USSR-Izv., 22:1 (1984), 181–189
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A. G. Vitushkin, “Real-analytic hypersurfaces in complex manifolds”, Russian Math. Surveys, 40:2 (1985), 1–35
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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
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N. G. Kruzhilin, “Local automorphisms and mappings of smooth strictly pseudoconvex hypersurfaces”, Math. USSR-Izv., 26:3 (1986), 531–552
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V. V. Ezhov, “Linearization of stability groups of a class of hypersurfaces”, Russian Math. Surveys, 41:3 (1986), 203–204
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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
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Michael Eastwood, Alexander Isaev, “Examples of unbounded homogeneous domains in complex space”, Sci China Ser A, 48:s1 (2005), 248
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