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Characterization of Domains in ℂn by their Noncompact Automorphism Groups

Published online by Cambridge University Press:  11 January 2016

Do Duc Thai  and
Ninh Van Thu
Do Duc Thai
Affiliation:
Department of Mathematics Hanoi National University of Education, 136 Xuan Thuy str., Hanoi, Vietnam, [email protected]
Ninh Van Thu
Affiliation:
Department of Mathematics, Mechanics and Informatics University of Natural Sciences, Hanoi National University, 334 Nguyen Trai str., Hanoi, Vietnam, [email protected]
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Abstract

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In this paper, the characterization of domains in ℂn by their noncompact automorphism groups are given.

Keywords

32M0532H0232H1532H50
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 196 , 2009 , pp. 135 - 160
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2009

References

[1] Bedford, E. and Pinchuk, S., Domains in C2 with noncompact groups of automorphisms, Math. USSR Sbornik, 63 (1989), 141–151.CrossRefGoogle Scholar
[2] Bedford, E. and Pinchuk, S., Domains in Cn+1 with noncompact automorphism group, J. Geom. Anal., 1 (1991), 165–191.CrossRefGoogle Scholar
[3] Bedford, E. and Pinchuk, S., Domains in C2 with noncompact automorphism groups, Indiana Univ. Math. Journal, 47 (1998), 199–222.CrossRefGoogle Scholar
[4] Bell, S., Local regularity of C.R. homeomorphisms, Duke Math. J., 57 (1988), 295–300.CrossRefGoogle Scholar
[5] Berteloot, F., Attraction de disques analytiques et continuité Holdérienne d’applications holomorphes propres, Topics in Compl. Anal., Banach Center Publ. (1995), 91–98.Google Scholar
[6] Berteloot, F., Characterization of models in C2 by their automorphism groups, Internat. J. Math., 5 (1994), 619–634.CrossRefGoogle Scholar
[7] Berteloot, F., Principle de Bloch et Estimations de la Metrique de Kobayashi des Domains de C2 , J. Geom. Anal. Math., 1 (2003), 29–37.Google Scholar
[8] Catlin, D., Estimates of invariant metrics on pseudoconvex domains of dimension two, Math. Z., 200 (1989), 429–466.Google Scholar
[9] Cho, S., A lower bound on the Kobayashi metric near a point of finite type in Cn , J. Geom. Anal., 2–4 (1992), 317–325.Google Scholar
[10] Cho, S., Boundary behavior of the Bergman kernal function on some pseudoconvex domains in Cn , Trans. of Amer. Math. Soc., 345 (1994), 803–817.Google Scholar
[11] D’Angelo, J. P., Real hypersurfaces, orders of contact, and applications, Ann. Math., 115 (1982), 615–637.Google Scholar
[12] Greene, R. and Krantz, S., Biholomorphic self-maps of domains, Lecture Notes in Math. 1276, 1987, pp. 136–207.Google Scholar
[13] Isaev, A. and Krantz, S., Domains with non-compact automorphism group: A survey, Adv. Math., 146 (1999), 1–38.Google Scholar
[14] Kobayashi, S., Hyperbolic Complex Spaces, Grundlehren der mathematischen Wis-senschaftenv. 318, Springer-Verlag, 1998.Google Scholar
[15] Narasimhan, R., Several Complex Variables, Chicago Lectures in Mathematics, University of Chicago Press, 1971.Google Scholar
[16] Pinchuk, S., The scaling method and holomorphic mappings, Proc. Symp. Pure Math. 52, Part 1, Amer. Math. Soc., 1991.Google Scholar
[17] Thai, D. D. and Minh, T. H., Generalizations of the theorems of Cartan and Greene-Krantz to complex manifolds, Illinois Jour. of Math., 48 (2004), 1367–1384.Google Scholar
[18] Wong, B., Characterization of the ball in Cn by its automorphism group, Invent. Math., 41 (1977), 253–257.CrossRefGoogle Scholar
[19] Rosay, J. P., Sur une caracterisation de la boule parmi les domaines de Cn par son groupe d’automorphismes, Ann. Inst. Fourier, 29 (4) (1979), 91–97.Google Scholar