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On Carathéodory completeness of pseudoconvex Reinhardt domains
Author(s):
Wlodzimierz
Zwonek
Journal:
Proc. Amer. Math. Soc.
128
(2000),
857-864.
MSC (1991):
Primary 32H15;
Secondary 32H20, 32F05
Posted:
July 28, 1999
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Abstract:
We give a complete characterization of Carathéodory complete pseudoconvex Reinhardt domains, which extends results of Pflug, Fu and the author.
References:
- [Car-Ceg-Wik]
- M. Carlehed, U. Cegrell & F. Wikström, Jensen Meauseres, Hyperconvexity and Boundary Behaviour of the Pluricomplex Green Function, Research Report No 15 Umea University (1997).
- [Fu]
- S. Fu, On completeness of invariant metrics of Reinhardt domains, Arch. Math. 63 (1994), 166-172. MR 95h:32024
- [Hay-Ken]
- W. K. Hayman & P. B. Kennedy, Subharmonic Functions, volume 1, London Mathematical Society Monographs 9, Academic Press, London, 1976. MR 57:665
- [Jar-Pfl]
- M. Jarnicki & P. Pflug, Invariant Distances and Metrics in Complex Analysis, Walter de Gruyter, 1993. MR 94k:32039
- [Kli]
- M. Klimek, Pluripotential Theory, Oxford Science Publications, 1991. MR 93h:32021
- [Kob]
- S. Kobayashi, Hyperbolic Manifolds and Holomorphic Mappings, Pure and Appl. Math. 2, M. Dekker, 1970. MR 43:3503
- [Lem]
- L. Lempert, La metrique de Kobayashi et la representation des domaines sur la boule, Bull. Soc. Math. France 109 (1981), 427-474. MR 84d:32036
- [Pfl]
- P. Pflug, About the Carathéodory completeness of all Reinhardt domains, In: Functional Analysis, Holomorphy and Approximation Theory II, (1984), 331-337, G. Zapata ed. MR 86b:32026
- [Ste]
- J. L. Stehlé, Fonctions plurisousharmoniques et convexité holomorphe de certaines fibrés analytiques. In, Séminaire Pierre Lelong (Analyse), Année 1973/1974 (ed. P. Lelong, P. Doulbeaut, H. Skoda) (1975), 155-179. MR 53:3368
- [Vla]
- V. Vladimirov, Methods of the Theory of Functions of Several Complex Variables. (Russian) Moskau 1964. English transl., Cambridge, Mass.-London, 1966. MR 34:1551
- [Zwo]
- W. Zwonek, On hyperbolicity of pseudoconvex Reinhardt domains, Arch. Math., to appear.
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Additional Information:
Wlodzimierz
Zwonek
Affiliation:
Instytut Matematyki, Reymonta 4, 30-059 Kraków, Poland
Address at time of publication:
Carl von Ossietzky Universität Oldenburg, Fachbereich 6 -- Mathematik, Postfach 2503, 26111 Oldenburg, Germany
Email:
zwonek@im.uj.edu.pl, zwonek@mathematik.uni-oldenburg.de
DOI:
10.1090/S0002-9939-99-05226-0
PII:
S 0002-9939(99)05226-0
Received by editor(s):
May 12, 1998.
Posted:
July 28, 1999
Additional Notes:
The author is a fellow of the Alexander von Humboldt Foundation.
Communicated by:
Steven R. Bell
Copyright of article:
Copyright
1999,
American Mathematical Society
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