Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-28T03:23:50.794Z Has data issue: false hasContentIssue false

Bergman completeness of unbounded hartogs Domains

Published online by Cambridge University Press:  11 January 2016

Peter Pflug
Affiliation:
Carl von Ossietzky Universität Oldenburg Institut für MathematikPostfach 2503 D-26111 [email protected]
Włodzimierz Zwonek
Affiliation:
Uniwersytet Jagielloński Instytut MatematykiReymonta 4 30-059Kraków [email protected]
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.

Some results for the Bergman functions in unbounded domains are shown. In particular, a class of unbounded Hartogs domains, which are Bergman complete and Bergman exhaustive, is given.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2005

References

[Bło 2004] Błocki, Z., The Bergman metric and the pluricomplex Green function, Trans. Amer. Math. Soc, 357 (2005), 26132625.Google Scholar
[Bło-Pfl 1998] Błocki, Z. and Pflug, P., Hyperconvexity and Bergman completeness, Nagoya Math. J., 151 (1998), 221225.Google Scholar
[Bre 1955] Bremermann, J., Holomorphic continuation of the kernel and the Bergman metric, Lectures on Functions of a Complex Variable, Univ. of Michigan Press (1955), pp. 349383.Google Scholar
[Chen 2004] Chen, B.-Y., Bergman completeness of hyperconvex manifolds, Nagoya Math. J., 175 (2004), 165170.Google Scholar
[Chen-Zhang 2002] Chen, B.-Y. and Zhang, J.-H., The Bergman metric on a Stein manifold with a bounded plurisubharmonic function, Trans. Amer. Math. Soc, 354 (2002), 2997-3009.Google Scholar
[Chen-Zhang 2004] Chen, B.-Y. and Zhang, J.-H., Addendum to ‘The Serre problem on certain bounded domains’, preprint.Google Scholar
[Chen-kam-ohs 2004] Chen, B.-Y., Kamimoto, J. and Ohsawa, T., Behavior of the Bergman kernel at infinity, Math. Z., 248 (2004), 695708.Google Scholar
[Her 1999] Herbort, G., The Bergman metric on hyperconvex domains, Math. Z., 232 (1999), 183196.Google Scholar
[Jar-pfl 1993] Jarnicki, M. and Pflug, P., Invariant Distances and Metrics in Complex Analysis, Walter de Gruyter, vol. 8, 1993.Google Scholar
[Jar-pfi-Zwo 2000] Jarnicki, M., Pflug, P. and Zwonek, W., On Bergman completeness of non-hyperconvex domains, Univ. Iag. Acta Math., 38 (2000), 169184.Google Scholar
[Juc 2004] Jucha, P., Bergman functions in C and Cn , Dissertation (in Polish) (2004).Google Scholar
[Kli 1991] Klimek, M., Pluripotential Theory, Oxford University Press, 1991.Google Scholar
[Kob 1962] Kobayashi, S., On complete Bergman metrics, Proc. Amer. Math. Soc., 13 (1962), 511513.Google Scholar
[Ohs 1993] Ohsawa, T., On the Bergman kernel of hyperconvex domains, Nagoya Math. J., 129 (1993), 4352.CrossRefGoogle Scholar
[Ohs-Tak 1987] Ohsawa, T. and Takegoshi, K., On the extension of L2-holomorphic functions, Math. Z., 195 (1987), 197204.Google Scholar
[Pfl-Zwo 2003] Pflug, P. and Zwonek, W., Logarithmic capacity and Bergman functions, Arch. Math. (Basel), 80 (2003), 536552.Google Scholar
[Ran 1995] Ransford, T., Potential Theory in the Complex Plane, Cambridge University Press, 1995.Google Scholar
[Zwo 1999] Zwonek, W., On Bergman completeness of pseudoconvex Reinhardt domains, Ann. Fac. Sci. Toulouse, 8 (1999), 537552.CrossRefGoogle Scholar
[Zwo 2000] Zwonek, W., Completeness, Reinhardt domains and the method of complex geodesics in the theory of invariant functions, Diss. Math., 388 (2000), 1103.Google Scholar
[Zwo 2002] Zwonek, W., Wiener’s type criterion for Bergman exhaustiveness, Bull. Pol. Acad.: Math., 50 (2002), 297311.Google Scholar