Abstract
In recent years, characterizations of certain classes of bounded pseudoconvex domains have been studied by several authors. In connection with these studies, let us consider the following problem about a characterization of bounded weakly pseudoconvex domains:
Let Ω be a bounded weakly pseudoconvex domain in ℂn as a model space and let D be an another bounded domain in ℂn. If D and Ω are locally biholomorphically equivalent near a boundary point where a holomorphic automorphism orbit of a point accumulates, then are they biholomorphically equivalent?
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Greene, R.E., Krantz, S.G.: Charcterizations of certain weakly pseudoconvex domains with non-compact automorphism groups. In: Krantz, S.G. (ed.) Complex analysis. Seminar, University Park PA, 1986. (Lect. Notes Math., vol. 1268, pp. 121-157) Berlin Heidelberg New York: Springer 1987
Kaneyuki, S.: Homogeneous bounded domains and Siegel domains. Lect. Notes Math., vol. 241, Berlin Heidelberg New York: Springer 1971
Kobayashi, S.: Hyperbolic manifolds and holomorphic mappings. New York: Marcel Dekker 1970
Kodama, A.: A characterization of certain domains with good boundary points in the sense of Greene and Krantz. Kodai Math. J. 12, 257–269 (1989)
Kodama, A.: A characterization of certain domains with good boundary points in the sense of Greene and Krantz, I. to appear in Tohoku Math. J.
Narasimhan, R.: Several complex variables. Chicago London: Univ. Chicago Press 1971
Vinberg, E.B., Gindikin, S.G., Pyatetzki-Shapiro, I.I.: Classification and canonical realization of complex bounded homogeneous domains. Trans. Moscow Math. Soc. 12, 404–437 (1963)
Rosay, J.P.: Sur une caractérisation de la boule parmi les domaines de ℂn par son groupe d’ automorphismes. Ann. Inst. Fourier (Grenoble) 29, 91–97 (1979)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig
About this paper
Cite this paper
Shimizu, S. (1991). A Characterization of Homogeneous Bounded Domains. In: Diederich, K. (eds) Complex Analysis. Aspects of Mathematics, vol 1. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-86856-5_40
Download citation
DOI: https://doi.org/10.1007/978-3-322-86856-5_40
Publisher Name: Vieweg+Teubner Verlag
Print ISBN: 978-3-322-86858-9
Online ISBN: 978-3-322-86856-5
eBook Packages: Springer Book Archive