A local version of Wong-Rosay’s theorem for proper holomorphic mappings

Ourimi, Nabil

doi:10.1090/S0002-9939-99-05428-3

A local version of Wong-Rosay’s theorem for proper holomorphic mappings
HTML articles powered by AMS MathViewer

by Nabil Ourimi PDF

Proc. Amer. Math. Soc. 128 (2000), 831-836 Request permission

Abstract:

In the present paper, we generalize Wong-Rosay’s theorem for proper holomorphic mappings with bounded multiplicity. As an application, we prove the non-existence of a proper holomorphic mapping from a bounded, homogenous domain in $\mathbb {C}^n$ onto a domain in $\mathbb {C}^n$ whose boundary contains strongly pseudoconvex points.

References

Eric Bedford, Proper holomorphic mappings from domains with real analytic boundary, Amer. J. Math. 106 (1984), no. 3, 745–760. MR 745150, DOI 10.2307/2374294
E. Bedford and S. Bell, Boundary behavior of proper holomorphic correspondences, Math. Ann. 272 (1985), no. 4, 505–518. MR 807287, DOI 10.1007/BF01455863
Eric Bedford and Steve Bell, Boundary continuity of proper holomorphic correspondences, Séminaire d’analyse P. Lelong-P. Dolbeault-H. Skoda, années 1983/1984, Lecture Notes in Math., vol. 1198, Springer, Berlin, 1986, pp. 47–64. MR 874760, DOI 10.1007/BFb0077042
François Berteloot, Un principe de localisation pour les domaines faiblement pseudoconvexes de $\textbf {C}^2$ dont le groupe d’automorphismes holomorphes n’est pas compact, Astérisque 217 (1993), 5, 13–27 (French, with French summary). Colloque d’Analyse Complexe et Géométrie (Marseille, 1992). MR 1247748
E. M. Chirka, Complex analytic sets, Mathematics and its Applications (Soviet Series), vol. 46, Kluwer Academic Publishers Group, Dordrecht, 1989. Translated from the Russian by R. A. M. Hoksbergen. MR 1111477, DOI 10.1007/978-94-009-2366-9
W. Klingenberg and S. Pinchuk, Normal families of proper holomorphic correspondences, Math. Z. 207 (1991), no. 1, 91–96. MR 1106815, DOI 10.1007/BF02571377
E. B. Lin and B. Wong, Curvature and proper holomorphic mappings between bounded domains in $\textbf {C}^n$, Rocky Mountain J. Math. 20 (1990), no. 1, 179–197. MR 1057987, DOI 10.1216/rmjm/1181073171
S.Pinchuk, Holomorphic inequivalences of somes classes of domains in $\mathbb {C}^n$, Math. USSR Sbornik. 39, (1981) 61-68.
K.Oeljeklaus and E.H.Youssfi, Proper holomorphic mappings and related automorphism groups, to appear in Journal of Geometric Analysis.
Jean-Pierre Rosay, Sur une caractérisation de la boule parmi les domaines de $\textbf {C}^{n}$ par son groupe d’automorphismes, Ann. Inst. Fourier (Grenoble) 29 (1979), no. 4, ix, 91–97 (French, with English summary). MR 558590
Walter Rudin, Proper holomorphic maps and finite reflection groups, Indiana Univ. Math. J. 31 (1982), no. 5, 701–720. MR 667790, DOI 10.1512/iumj.1982.31.31050
Karl Stein, Maximale holomorphe und meromorphe Abbildungen. II, Amer. J. Math. 86 (1964), 823–868 (German). MR 171030, DOI 10.2307/2373159
Karl Stein, Topics on holomorphic correspondences, Rocky Mountain J. Math. 2 (1972), no. 3, 443–463. MR 311945, DOI 10.1216/RMJ-1972-2-3-443
Vasiliĭ Sergeevič Vladimirov, Methods of the theory of functions of many complex variables, The M.I.T. Press, Cambridge, Mass.-London, 1966. Translated from the Russian by Scripta Technica, Inc; Translation edited by Leon Ehrenpreis. MR 0201669
B. Wong, Characterization of the unit ball in $\textbf {C}^{n}$ by its automorphism group, Invent. Math. 41 (1977), no. 3, 253–257. MR 492401, DOI 10.1007/BF01403050