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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
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Abstract:
We give an example of a bounded pseudoconvex domain in , the Wu metric of which (associated to the Kobayashi-Royden or the Azukawa metric) is not upper semicontinuous.
References:
-
- [Che-Kim 1]
- C. K. Cheung, K. T. Kim, Analysis of the Wu metric. I: The case of convex Thullen domains, Trans. Amer. Math. Soc. 348 (1996), 1421-1457. MR 1357392 (96i:32026)
- [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- H. Wu, Unpublished notes.
- [Wu 2]
- H. Wu, Old and new invariant metrics on complex manifolds, in: Several Complex Variables, J. E. Fornæss (ed.), Math. Notes 38, Princeton Univ. Press, 1993, 640-682. MR 1207887 (94a:32038)
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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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