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ISSN 1088-6826(e) ISSN 0002-9939(p)

The Wu metric is not upper semicontinuous

Author(s): Piotr Jucha
Journal: Proc. Amer. Math. Soc. 136 (2008), 1349-1358.
MSC (2000): Primary 32F45
Posted: December 18, 2007
MathSciNet review: 2367108
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Abstract | References | Similar articles | Additional information

Abstract: We give an example of a bounded pseudoconvex domain in $\mathbb{C}^n$ , the Wu metric of which (associated to the Kobayashi-Royden or the Azukawa metric) is not upper semicontinuous.

References:

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[Che-Kim 2]: C. K. Cheung, K. T. Kim, Analysis of the Wu metric. II: The case of non-convex Thullen domains, Proc. Amer. Math. Soc. 125 (1997), 1131-1142. MR 1363414 (97f:32029)
[Jar-Pfl 1]: M. Jarnicki, P. Pflug, Invariant Distances and Metrics in Complex Analysis, de Gruyter Exp. Math. 9, de Gruyter, Berlin, 1993. MR 1242120 (94k:32039)
[Jar-Pfl 2]: M. Jarnicki, P. Pflug, Invariant distances and metrics in complex analysis--revisited, Dissertationes Math. 430 (2003). MR 2167637 (2006h:32010)
[Jar-Pfl 3]: M. Jarnicki, P. Pflug, On the upper semicontinuity of the Wu metric, Proc. Amer. Math. Soc. 133 (2005), 239-244. MR 2086216 (2005g:32012)
[Juc]: P. Jucha, The Wu metric in elementary Reinhardt domains, Univ. Iagel. Acta Math. 38 (2000), 169-184. MR 1962715 (2003m:32008)
[Wu 1]: H. Wu, Unpublished notes.
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Additional Information:

Piotr Jucha
Affiliation: Institute of Mathematics, Jagiellonian University, Reymonta 4, 30--059 Kraków, Poland
Email: Piotr.Jucha@im.uj.edu.pl

DOI: 10.1090/S0002-9939-07-09135-6
PII: S 0002-9939(07)09135-6
Keywords: Wu metric, invariant metrics
Received by editor(s): October 13, 2006
Received by editor(s) in revised form: February 12, 2007
Posted: December 18, 2007
Additional Notes: This work was supported by Research Grant No.~1~PO3A~005~28 of the Polish Ministry of Science and Higher Education.
Communicated by: Mei-Chi Shaw
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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