Nagoya Mathematical Journal

An example concerning Bergman completeness

Włodzimierz Zwonek

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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.

Article information

Nagoya Math. J., Volume 164 (2001), 89-101.

First available in Project Euclid: 27 April 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 32F45: Invariant metrics and pseudodistances
Secondary: 32A25: Integral representations; canonical kernels (Szego, Bergman, etc.) 32A36: Bergman spaces


Zwonek, Włodzimierz. An example concerning Bergman completeness. Nagoya Math. J. 164 (2001), 89--101.

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