On continuous extension and rigidity of holomorphic mappings between domains with piecewise smooth boundaries
Sbornik. Mathematics, Tome 82 (1995) no. 2, pp. 471-483 Cet article a éte moissonné depuis la source Math-Net.Ru

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A theorem is proved concerning the boundary continuity of holomorphic mappings between domains with piecewise smooth strictly pseudoconvex boundaries in $\mathbb{C}^n$. This theorem is used to establish results on nonexistence of proper holomorphic mappings between certain classes of domains.
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A. B. Sukhov. On continuous extension and rigidity of holomorphic mappings between domains with piecewise smooth boundaries. Sbornik. Mathematics, Tome 82 (1995) no. 2, pp. 471-483. http://geodesic.mathdoc.fr/item/SM_1995_82_2_a13/

[1] Lelon P., Gruman L., Tselye funktsii mnogikh kompleksnykh peremennykh, Mir, M., 1989 | MR | Zbl

[2] Margulis G. A., “Sootvetstvie granits pri bigolomorfnykh otobrazheniyakh mnogomernykh oblastei”, Tezisy dokl. Vses. konf. po teorii funktsii kompleksnogo peremennogo, Kharkov, 1971, 137–138

[3] Pinchuk S. I., “Granichnaya teorema edinstvennosti dlya golomorfnykh funktsii neskolkikh kompleksnykh peremennykh”, Matem. zametki, 15:2 (1974), 205–212 | MR | Zbl

[4] Pinchuk S. I., “O sobstvennykh golomorfnykh otobrazheniyakh strogo psevdovypuklykh oblastei”, Sib. matem. zhurn., 15:4 (1974), 909–917 | MR | Zbl

[5] Pinchuk S. I., “Golomorfnaya neekvivalentnost nekotorykh klassov oblastei v ${\mathbb C}^n$”, Matem. sb., 111 (153) (1980), 67–94 | MR | Zbl

[6] Pinchuk S. I., “Golomorfnye otobrazheniya v ${\mathbb C}^n$ i problema golomorfnoi ekvivalentnosti”, Itogi nauki i tekhniki. Sovremennye problemy matematiki. Fundamentalnye napravleniya, 9, VINITI, M., 1986, 197–224

[7] Pinchuk S. I., Tsyganov Sh. I., “Gladkost $\operatorname {CR}$-otobrazhenii mezhdu strogo psevdovypuklymi giperpoverkhnostnymi”, Izv. AN SSSR. Ser. matem., 53:5 (1989), 1120–1129

[8] Poletskii E. A., Shabat B. V., “Invariantnye metriki”, Itogi nauki i tekhniki. Sovremennye problemy matematiki. Fundamentalnye napravleniya, 9, VINITI, M., 1986, 73–125 | MR

[9] Pyatetskii-Shapiro I. I., Geometriya klassicheskikh oblastei i teoriya avtomorfnykh funktsii, Nauka, M., 1961

[10] Rudin U., Teoriya funktsii v edinichnom share iz ${\mathbb C}^n$, Mir, M., 1984 | MR | Zbl

[11] Sadullaev A., “Granichnaya teorema edinstvennosti v ${\mathbb C}^n$”, Matem. sb., 101 (143) (1976), 568–583 | MR | Zbl

[12] Khenkin G. M., “Analiticheskii poliedr golomorfno neekvivalenten strogo psevdovypukloi oblasti”, DAN SSSR, 210:5 (1973), 1026–1029 | MR | Zbl

[13] Khenkin G. M., Chirka E. M., “Granichnye svoistva golomorfnykh funktsii neskolkikh kompleksnykh peremennykh”, Itogi nauki i tekhniki. Sovremennye problemy matematiki, 4, VINITI, M., 1975, 13–112

[14] Chirka E. M., Kompleksnye analiticheskie mnozhestva, Nauka, M., 1985 | MR

[15] Shabat B. V., Vvedenie v kompleksnyi analiz, T. 2, Nauka, M., 1985 | MR

[16] Berteloot F., “Holder continuity of proper holomorphic mappings”, Studia Mathematica, 100:3 (1991), 229–235 | MR | Zbl

[17] Berteloot F., “A remark on local continuous extension of holomorphic mappings”, Contemporary Math., 137 (1992), 79–83 | MR | Zbl

[18] Berteloot F., Attraction des disques analytiques et continuite Holderienne d'applications holomorphes propres, Preprint, 1993 | Zbl

[19] Burns D. jr., Shnider S., Wells R. O. Jr., “Deformations of strictly pseudoconvex domains”, Invent. math., 46:3 (1978), 327–253 | DOI | MR

[20] Coupet B., “Construction de disques analytiques et regularite de fonctions holomorphes au bord”, Math. Z., 209 (1992), 179–204 | DOI | MR | Zbl

[21] Diederich K., Fornaess J. E., “Proper holomorphic maps onto pseudoconvex domains with real analytic boundary”, Ann. Math., 110:3 (1979), 575–592 | DOI | MR | Zbl

[22] Fornaess J. E., Løw E., “Proper holomorphic mappings”, Math. Scand., 58 (1986), 311–322 | MR | Zbl

[23] Forstneric F., Rosay J.-P., “Localization of the Kobayashi metric and the boundary continuity of proper holomorphic mappings”, Math. Ann., 279 (1987), 239–252 | DOI | MR | Zbl

[24] Forstneric F., “Mappings of strongly pseudoconvex Cauchy–Riemann manifolds”, Proc. Symp. Pure Math., Part 1, 52 (1991), 59–92 | MR | Zbl

[25] Graham I., “Boundary behaviour of the Caratheodory and Kobayashi metrics on strongly pseudoconvex domains in ${\mathbb C}^n$ with smooth boundary”, Trans. Amer. Math. Soc., 207 (1975), 219–290 | DOI | MR

[26] Pinchuk S. I., “The scaling method and holomorphic mappings”, Proc. Symp. Pure Math., Part 1, 52 (1991), 151–161 | MR | Zbl

[27] Poincare H., “Les fonctions analytiques de deux variables et la representation conform”, Rend. Circ. mat. Palermo, 23 (1907), 185–220 | DOI | Zbl

[28] Range M., “On the topological extension to the boundary of biholomorphic maps in ${\mathbb C}^n$”, Trans. Amer. Math. Soc., 216 (1976), 203–216 | DOI | MR | Zbl

[29] Royden H. L., “Remarks on the Kobayshi metric”, Several complex variables, Proc. Int. Conf. Univ. of Maryland, V. II (1970), Lect. Notes Math., 185, 1971 | MR

[30] Sibony N., “A class of hyperbolic manifolds”, Ann. Math. Stud., 100 (1981), 357–372 | MR | Zbl

[31] Vormoor N., “Topologische Fortsetzung biholomorpher Funktionen auf dem Rand bet beschrankten streng-pseudokonvexeten Gebieten in ${\mathbb C}^n$”, Math. Ann., 204 (1973), 239–261 | DOI | MR | Zbl