Geodesic
Holomorphic extension of mappings of compact hypersurfaces
Izvestiya. Mathematics, Tome 20 (1983) no. 1, pp. 27-33 
A. G. Vitushkin. Holomorphic extension of mappings of compact hypersurfaces. Izvestiya. Mathematics, Tome 20 (1983) no. 1, pp. 27-33. http://geodesic.mathdoc.fr/item/IM2_1983_20_1_a1/
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     author = {A. G. Vitushkin},
     title = {Holomorphic extension of mappings of compact hypersurfaces},
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     url = {http://geodesic.mathdoc.fr/item/IM2_1983_20_1_a1/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Beloshapka V., Vitushkin A., “Otsenki radiusa skhodimosti stepennykh ryadov, zadayuschikh otobrazhenie analiticheskikh giperpoverkhnostei”, Izv. AN SSSR. Ser. matem., 45:5 (1981), 962–984 | MR | Zbl

[2] Loboda A., “O lokalnykh avtomorfizmakh veschestvenno analiticheskikh giperpoverkhnostei”, Izv. AN SSSR. Ser. matem., 45:3 (1981), 620–645 | MR | Zbl

[3] Pinchuk S., “O golomorfnykh otobrazheniyakh veschestvenno-analiticheskikh giperpoverkhnostei”, Matem. sb., 105(147):4 (1978), 574–593 | MR | Zbl

[4] Chern S., Moser I., “Real hypersurfaces in complex manyfolds”, Acta Math., 133:134 (1974), 219–271 | DOI | MR