Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-27T22:22:12.634Z Has data issue: false hasContentIssue false

An example concerning Bergman completeness

Published online by Cambridge University Press:  22 January 2016

Włodzimierz Zwonek*
Affiliation:
Instytut Matematyki, Uniwersytet Jagielloński, Reymonta 4, 30-059 Kraków, Poland, zwonek@im.uj.edu.pl
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We construct a bounded plane domain which is Bergman complete but for which the Bergman kernel does not tend to infinity as the point approaches the boundary.

Keywords

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2001

References

[Blo-Pfl] Blocki, Z. & Pflug, P., Hyperconvexity and Bergman completeness, Nagoya Math. J., 151 (1998), 221-225.CrossRefGoogle Scholar
[Chen 1] Chen, B.-Y., Completeness of the Bergman metric on non-smooth pseudo-convex domains, Ann. Polon. Math., LXXI (3) (1999), 242-251.Google Scholar
[Chen 2] Chen, B.-Y., A remark on the Bergman completeness, Complex Variables Theory Appl., 42 (2000), no.1, 11-15.Google Scholar
[Her] Herbort, G., The Bergman metric on hyperconvex domains, Math. Z., 232(1) (1999), 183-196.Google Scholar
[Jar-Pfl ] Jarnicki, M. & Pflug, P., Invariant Distances and Metrics in Complex Analysis, Walter de Gruyter, Berlin, 1993.Google Scholar
[Jar-Pfl-Zwo] Jarnicki, M., Pflug, P. & Zwonek, W., On Bergman completeness of non-hyperconvex domains, Univ. Iag. Acta Math., No.38 (2000), 169-184.Google Scholar
[Ohs 1] Ohsawa, T., Boundary behaviour of the Bergman kernel function on pseu-doconvex domains, Publ. RIMS Kyoto Univ., 20 (1984), 897-902.CrossRefGoogle Scholar
[Ohs 2] Ohsawa, T., On the Bergman kernel of hyperconvex domains, Nagoya Math. J., 129 (1993), 43-52.Google Scholar
[Pfl] Pflug, P., Various applications of the existence of well growing holomorphic functions, Functional Analysis, Holomorphy and Approximation Theory, J. A. Barossa (ed.), Math. Studies, 71 (1982), North-Holland.Google Scholar
[Zwo] Zwonek, W., On Bergman completeness of pseudoconvex Reinhardt domains, Ann. Fac. Sci. Toul., VIII (3) (1999), 537-552.Google Scholar