Nagoya Mathematical Journal

Bergman completeness of unbounded Hartogs domains

Peter Pflug and Włodzimierz Zwonek

Full-text: Open access

Abstract

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.

Article information

Source
Nagoya Math. J., Volume 180 (2005), 121-133.

Dates
First available in Project Euclid: 14 December 2005

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1134569899

Mathematical Reviews number (MathSciNet)
MR2186672

Zentralblatt MATH identifier
1094.32004

Subjects
Primary: 32A07: Special domains (Reinhardt, Hartogs, circular, tube) 32F45: Invariant metrics and pseudodistances 32A25: Integral representations; canonical kernels (Szego, Bergman, etc.)
Secondary: 32U35: Pluricomplex Green functions 30C85: Capacity and harmonic measure in the complex plane [See also 31A15]

Citation

Pflug, Peter; Zwonek, Włodzimierz. Bergman completeness of unbounded Hartogs domains. Nagoya Math. J. 180 (2005), 121--133. https://projecteuclid.org/euclid.nmj/1134569899


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References

  • Z. Błocki, The Bergman metric and the pluricomplex Green function , Trans. Amer. Math. Soc., 357 (2005), 2613–2625.
  • Z. Błocki and P. Pflug, Hyperconvexity and Bergman completeness , Nagoya Math. J., 151 (1998), 221–225.
  • J. Bremermann, Holomorphic continuation of the kernel and the Bergman metric , Lectures on Functions of a Complex Variable, Univ. of Michigan Press (1955), 349–383.
  • B.-Y. Chen, Bergman completeness of hyperconvex manifolds , Nagoya Math. J., 175 (2004), 165–170.
  • B.-Y. Chen and J.-H. Zhang, The Bergman metric on a Stein manifold with a bounded plurisubharmonic function , Trans. Amer. Math. Soc., 354 (2002), 2997–3009.
  • B.-Y. Chen and J.-H. Zhang, Addendum to `The Serre problem on certain bounded domains' , preprint.
  • B.-Y. Chen, J. Kamimoto and T. Ohsawa, Behavior of the Bergman kernel at infinity , Math. Z., 248 (2004), 695–708.
  • G. Herbort, The Bergman metric on hyperconvex domains , Math. Z., 232 (1999), 183–196.
  • M. Jarnicki and P. Pflug, Invariant Distances and Metrics in Complex Analysis, Walter de Gruyter, vol. 8 (1993).
  • M. Jarnicki, P. Pflug and W. Zwonek, On Bergman completeness of non-hyperconvex domains , Univ. Iag. Acta Math., 38 (2000), 169–184.
  • P. Jucha, Bergman functions in $\mathbbC$ and $\mathbbC^n$ , Dissertation (in Polish) (2004).
  • M. Klimek, Pluripotential Theory, Oxford University Press (1991).
  • S. Kobayashi, On complete Bergman metrics , Proc. Amer. Math. Soc., 13 (1962), 511–513.
  • T. Ohsawa, On the Bergman kernel of hyperconvex domains , Nagoya Math. J., 129 (1993), 43–52.
  • T. Ohsawa and K. Takegoshi, On the extension of $L^2$-holomorphic functions , Math. Z., 195 (1987), 197–204.
  • P. Pflug and W. Zwonek, Logarithmic capacity and Bergman functions , Arch. Math. (Basel), 80 (2003), 536–552.
  • T. Ransford, Potential Theory in the Complex Plane, Cambridge University Press (1995).
  • W. Zwonek, On Bergman completeness of pseudoconvex Reinhardt domains , Ann. Fac. Sci. Toulouse, 8 (1999), 537–552.
  • W. Zwonek, Completeness, Reinhardt domains and the method of complex geodesics in the theory of invariant functions , Diss. Math., 388 (2000), 1–103.
  • W. Zwonek, Wiener's type criterion for Bergman exhaustiveness , Bull. Pol. Acad\.: Math., 50 (2002), 297–311.