Geodesic
Finite-dimensionality of the group of $CR$ automorphisms of a standard $CR$ manifold, and proper holomorphic mappings of Siegel domains
Izvestiya. Mathematics, Tome 32 (1989) no. 3, pp. 655-662 
A. E. Tumanov. Finite-dimensionality of the group of $CR$ automorphisms of a standard $CR$ manifold, and proper holomorphic mappings of Siegel domains. Izvestiya. Mathematics, Tome 32 (1989) no. 3, pp. 655-662. http://geodesic.mathdoc.fr/item/IM2_1989_32_3_a9/
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It is shown that local $CR$ automorphisms of nondegenerate standard $CR$ manifolds are rational and form a finite-dimensional Lie group. It is established that proper holomorphic mappings of nondegenerate Siegel domains are biholomorphic and rational. Bibliography: 14 titles.

[1] Tumanov A. E., Geometriya $CR$-mnogoobrazii, Sovremennye problemy matematiki. Fundamentalnye napravleniya, 9, VINITI, M., 1986

[2] Naruki I., “Holomorphic extension problem for standard real submanifolds of second kind”, Publ. Res. Inst. Math. Kyoto Univ., 6 (1970), 113–187 | DOI | MR | Zbl

[3] Tumanov A. E., Khenkin G. M., “Lokalnaya kharakterizatsiya golomorfnykh avtomorfizmov oblastei Zigelya”, Funktsion. analiz, 17:4 (1983), 49–81 | MR

[4] Tanaka N., “On infinitesimal automorphisms of Siegel domains”, J. Math. Soc. Japan, 22:2 (1970), 180–212 | MR | Zbl

[5] Tumanov A. E., Khenkin G. M., “Sobstvennye otobrazheniya oblastei Zigelya”, Kompleksnye metody v matematicheskoi fizike. Vsesoyuznaya shkola molodykh uchenykh, Donetsk, 1984, 185

[6] Airapetyan R. A., Khenkin G. M., “Integralnye predstavleniya differentsialnykh form na mnogoobraziyakh Koshi–Rimana i teoriya $CR$-funktsii, II”, Matem. sb., 127:1 (1985), 92–112 | MR | Zbl

[7] Webster S. M., “Holomorphic mappings of domains with generic corners”, Proc. Amer. Math. Soc., 86:2 (1982), 236–240 | DOI | MR | Zbl

[8] Pyatetskii-Shapiro I. I., Geometriya klassicheskikh oblastei i teoriya avtomorfnykh funktsii, Nauka, M., 1961, 191 pp. | MR

[9] Alexander H., “Holomorphic mappings from the ball and polydisc”, Math. Ann., 209 (1974), 249–256 | DOI | MR | Zbl

[10] Bell S., “Proper holomorphic mapping and the Bergman projection”, Duke Math. J., 48:1 (1981), 167–175 | DOI | MR | Zbl

[11] Bell S., “Proper holomorphic mapping between circular domains”, Comm. Math. Helv., 57:4 (1982), 532–538 | DOI | MR | Zbl

[12] Tumanov A. E., Khenkin G. M., “Lokalnaya kharakterizatsiya analiticheskikh avtomorfizmov klassicheskikh oblastei”, Dokl. AN SSSR, 267:4 (1982), 794–796 | MR

[13] Fuks B. A., Spetsialnye glavy teorii analiticheskikh funktsii mnogikh kompleksnykh peremennykh, Nauka, M., 1983, 427 pp. | Zbl

[14] Beloshapka V. K., “Konechnomernost gruppy avtomorfizmov veschestvenno analiticheskoi poverkhnosti”, Izv. AN SSSR. Ser. matem., 52:2 (1988), 437–442 | MR | Zbl