Geodesic
Holomorphic extension of mappings of compact hypersurfaces
Izvestiya. Mathematics , Tome 20 (1983) no. 1, pp. 27-33.

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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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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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[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

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