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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On Carathéodory completeness of pseudoconvex Reinhardt domains
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by Włodzimierz Zwonek PDF
Proc. Amer. Math. Soc. 128 (2000), 857-864 Request permission

Abstract:

We give a complete characterization of Carathéodory complete pseudoconvex Reinhardt domains, which extends results of Pflug, Fu and the author.
References
  • M. Carlehed, U. Cegrell & F. Wikström, Jensen Meauseres, Hyperconvexity and Boundary Behaviour of the Pluricomplex Green Function, Research Report No 15 Umea University (1997).
  • Siqi Fu, On completeness of invariant metrics of Reinhardt domains, Arch. Math. (Basel) 63 (1994), no. 2, 166–172. MR 1289299, DOI 10.1007/BF01189891
  • W. K. Hayman and P. B. Kennedy, Subharmonic functions. Vol. I, London Mathematical Society Monographs, No. 9, Academic Press [Harcourt Brace Jovanovich, Publishers], London-New York, 1976. MR 0460672
  • Marek Jarnicki and Peter Pflug, Invariant distances and metrics in complex analysis, De Gruyter Expositions in Mathematics, vol. 9, Walter de Gruyter & Co., Berlin, 1993. MR 1242120, DOI 10.1515/9783110870312
  • Maciej Klimek, Pluripotential theory, London Mathematical Society Monographs. New Series, vol. 6, The Clarendon Press, Oxford University Press, New York, 1991. Oxford Science Publications. MR 1150978
  • Shoshichi Kobayashi, Hyperbolic manifolds and holomorphic mappings, Pure and Applied Mathematics, vol. 2, Marcel Dekker, Inc., New York, 1970. MR 0277770
  • László Lempert, La métrique de Kobayashi et la représentation des domaines sur la boule, Bull. Soc. Math. France 109 (1981), no. 4, 427–474 (French, with English summary). MR 660145
  • Peter Pflug, About the Carathéodory completeness of all Reinhardt domains, Functional analysis, holomorphy and approximation theory, II (Rio de Janeiro, 1981) North-Holland Math. Stud., vol. 86, North-Holland, Amsterdam, 1984, pp. 331–337. MR 771335, DOI 10.1016/S0304-0208(08)70835-1
  • Jean-Luc Stehlé, Fonctions plurisousharmoniques et convexité holomorphe de certains fibrés analytiques, Séminaire Pierre Lelong (Analyse), Année 1973–1974, Lecture Notes in Math., Vol. 474, Springer, Berlin, 1975, pp. 155–179 (French). MR 0399524
  • 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
  • W. Zwonek, On hyperbolicity of pseudoconvex Reinhardt domains, Arch. Math., to appear.
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Additional Information
  • Włodzimierz 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
  • Received by editor(s): May 12, 1998
  • Published electronically: July 28, 1999
  • Additional Notes: The author is a fellow of the Alexander von Humboldt Foundation.
  • Communicated by: Steven R. Bell
  • © Copyright 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 128 (2000), 857-864
  • MSC (1991): Primary 32H15; Secondary 32H20, 32F05
  • DOI: https://doi.org/10.1090/S0002-9939-99-05226-0
  • MathSciNet review: 1646214