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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The Lempert function of the symmetrized polydisc in higher dimensions is not a distance


Authors: Nikolai Nikolov, Peter Pflug and Wlodzimierz Zwonek
Journal: Proc. Amer. Math. Soc. 135 (2007), 2921-2928
MSC (2000): Primary 32F45
Published electronically: May 10, 2007
MathSciNet review: 2317970
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Abstract: We prove that the Lempert function of the symmetrized polydisc in dimension greater than two is not a distance.


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Additional Information

Nikolai Nikolov
Affiliation: Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria
Email: nik@math.bas.bg

Peter Pflug
Affiliation: Carl von Ossietzky Universität Oldenburg, Fachbereich Mathematik, Postfach 2503, D-26111 Oldenburg, Germany
Email: pflug@mathematik.uni-oldenburg.de

Wlodzimierz Zwonek
Affiliation: Instytut Matematyki, Uniwersytet Jagielloński, Reymonta 4, 30-059 Kraków, Poland
Email: Wlodzimierz.Zwonek@im.uj.edu.pl

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08817-X
PII: S 0002-9939(07)08817-X
Keywords: Symmetrized polydisc, Carath\'eodory distance and metric, Kobayashi distance and metric, Lempert function
Received by editor(s): January 31, 2006
Received by editor(s) in revised form: June 9, 2006
Published electronically: May 10, 2007
Additional Notes: This paper was written during the stays of the first and third named authors at Universität Oldenburg supported by grants from the DFG (January – March 2006 and November 2005 (DFG Projekt 227/8-1/2)). They would like to thank both institutions for their support. The third author was also supported by the Research Grant No. 1 PO3A 005 28, which is financed by public means in the programme promoting science in Poland in the years 2005-2008.
The authors thank the referee for his remarks which essentially improved this paper.
Communicated by: Mei-Chi Shaw
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.