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JOURNALS // Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya // Archive

Izv. Akad. Nauk SSSR Ser. Mat., 1982 Volume 46, Issue 1, Pages 28–35 (Mi im1603)

This article is cited in 10 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.

UDC: 517.5

MSC: Primary 32D15; Secondary 32H99, 32C05

Received: 18.09.1981


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

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© Steklov Math. Inst. of RAS, 2024