Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-19T10:38:54.103Z Has data issue: false hasContentIssue false
  • English
  • Français

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]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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