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On an example concerning
the Kobayashi pseudodistance


Author: Wlodzimierz Zwonek
Journal: Proc. Amer. Math. Soc. 126 (1998), 2945-2948
MSC (1991): Primary 32H15
DOI: https://doi.org/10.1090/S0002-9939-98-04419-0
MathSciNet review: 1452838
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Abstract: In this short note we calculate the Kobayashi pseudodistance for elementary Reinhardt domains in $\mathbb{C}^{2}$. They deliver us a number of examples giving a negative answer to a problem posed by S. Kobayashi.


References [Enhancements On Off] (What's this?)

  • [HW] G. H. Hardy & E. M. Wright, An Introduction to the Theory of Numbers, Oxford Science Publ., 1978. MR 81i:10002
  • [JP] M. Jarnicki & P. Pflug, Invariant Distances and Metrics in Complex Analysis, Walter de Gruyter, 1993. MR 94k:32039
  • [K] S. Kobayashi, Hyperbolic Manifolds and Holomorphic Mappings, Pure and Appl. Math. 2, M. Dekker, 1970. MR 43:3503
  • [L] L. Lempert, La métrique de Kobayashi et la représentation des domaines sur la boulle, Bull. Soc. Math. France 109 (1981), 427-479. MR 84d:32036
  • [PZ] P. Pflug & W. Zwonek, Effective formulas for invariant functions - case of elementary Reinhardt domains, (preprint).

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Additional Information

Wlodzimierz Zwonek
Affiliation: Instytut Matematyki, Uniwersytet Jagielloński, 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: https://doi.org/10.1090/S0002-9939-98-04419-0
Received by editor(s): February 28, 1997
Additional Notes: The paper was partially supported by the KBN grant No 2 PO3A 060 08.
Communicated by: Steven R. Bell
Article copyright: © Copyright 1998 American Mathematical Society

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