On an example concerning the Kobayashi pseudodistance
HTML articles powered by AMS MathViewer
- by Włodzimierz Zwonek PDF
- Proc. Amer. Math. Soc. 126 (1998), 2945-2948 Request permission
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
- G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, 5th ed., The Clarendon Press, Oxford University Press, New York, 1979. MR 568909
- 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
- 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, DOI 10.24033/bsmf.1948
- P. Pflug & W. Zwonek, Effective formulas for invariant functions – case of elementary Reinhardt domains, (preprint).
Additional Information
- Włodzimierz 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
- 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
- © Copyright 1998 American Mathematical Society
- 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