Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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A METRIC INDUCED BY THE BERGMAN KERNEL

  • Kim, Jong Jin (Department of Mathematics and Institute of Pure and Applied Mathematics, Chonbuk National University)
  • Received : 2014.10.08
  • Accepted : 2014.11.07
  • Published : 2014.12.25
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Abstract

In this paper, we define a metric induced by the Bergman Kernel and prove a property that the metric has under any biholomorphic mapping.

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References

  1. N. Aronszajn, The theory of reproducing kernel, Trans. AMS. 68 (1950), 337-404. https://doi.org/10.1090/S0002-9947-1950-0051437-7
  2. J. Bremermann, "Holomorphic continuation of the kernel and the Bergman metric" in Lectures on functions of a complex variables, Univ. of Mich. Press (1955), 349-383.
  3. I. Graham, Boundary behavior of the Caratheodory and Kobayashi metrics on Strongly Pseudoconvex Domains in $\mathbb{C}^n$ with smooth boundary, Trans. AMS. 207 (1975), 219-240.
  4. M. Jarnicki and P. Pflug, Invariant Distances and Metrics in Complex Analysis, Walter de Gruyter, Berlin, New York, 1993.
  5. M. Jarnicki and P. Pflug, First Steps in Several Complex Variables: Reinhardt Domains, European Mathematical Society, 2008.
  6. J.J. Kim On the singular Kobayashi pseudometrics, Honam Math. Journal 29(4) (2007), 617-630. https://doi.org/10.5831/HMJ.2007.29.4.617
  7. L. Lempert, La metrique de Kobayashi et la representation des domaines sur la boule, Bull. Soc. Math. France 109 (1981), 427-474.
  8. N. Nikolov, Stability and boundary behavior of the Kobayashi metrics, Acta Math. Hungar. 90(4) (2001), 283-291. https://doi.org/10.1023/A:1010685812973
  9. H. L. Royden, "Remarkes on the Kobayashi metric" in Proceedings of the Mary-land Conference on Several Complex Variables II, Lecture Notes in Math. 189, Springer-Verlag (1971), 125-137.
  10. So-chin Chen and Mei-chi Shaw, Partial Differential Equations in Several Complex Variables, Studies in Advanced Mathematics, AMS. 19 (2001).
  11. J. Yu, "Singular Kobayashi metrics and finite type conditions", Proc. AMS. 123 (1995).