Geodesic
Extension of locally biholomorphic mappings of domains into complex projective space
Izvestiya. Mathematics , Tome 22 (1984) no. 1, pp. 181-189.

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In this paper it is proved that every locally biholomorphic mapping of a domain $D\subset\mathbf C^n$ into $\mathbf C\mathrm P^n$ can be extended to a biholomorphic mapping of the envelope of holomorphy $\widetilde D$ into $\mathbf C\mathrm P^n$. Corollaries are presented for extending mappings of hypersurfaces with indefinite Levi form. Bibliography: 12 titles 
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S. M. Ivashkovich. Extension of locally biholomorphic mappings of domains into complex projective space. Izvestiya. Mathematics , Tome 22 (1984) no. 1, pp. 181-189. http://geodesic.mathdoc.fr/item/IM2_1984_22_1_a6/

[1] Adachi K., Suzuki M., Ioshida M., “Continuation of holomorphic mappings, with values in complex Lie group”, Pacif. J. Math., 47:1 (1973), 1–4 | MR | Zbl

[2] Bochner S., Montgomery D., “Groups on analytic manibolds”, Ann. Math., II Ser., 48 (1947), 659–669 | DOI | MR | Zbl

[3] Vitushkin A. G., “Golomorfnoe prodolzhenie otobrazhenii kompaktnykh giperpoverkhnostei”, Izv. AN SSSR. Ser. matem., 46:1 (1982), 28–35 | MR

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

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

[6] Vitushkin A. G., Ivashkovich S. M., “O prodolzhenii golomorfnykh otobrazhenii veschestvenno-analiticheskikh giperpoverkhnostei v kompleksnoe proektivnoe prostranstvo”, Dokl. AN SSSR, 267:6 (1982), 1853–1854 | MR

[7] Griffits P., “Iwo theorem on extension of holomorphic mappings”, Invent. Math., 14:1 (1971), 27–62 | DOI | MR

[8] Hirschowitz A., “Un exemple concernant le prolongement analytique”, C.R. Acad. Sci. Paris, 275:23 (1972), 1231–1233 | MR | Zbl

[9] Kajiwara J., Sakai E., “Generalization of Levi–Oka's theorem concerning meromorphic functions”, Nagoya Math., J., 29 (1967), 75–84 | MR | Zbl

[10] Shiftman B., “Extension of holomorphic maps into hermitian manifolds”, Math. Ann., 194:4 (1971), 249–258 | DOI | MR

[11] Mamford D., Algebraicheskaya geometriya, Mir, M., 1980

[12] Khermander L., Vvedenie v teoriyu funktsii neskolkikh kompleksnykh peremennykh, Mir, M., 1968 | MR