Skip to main content
SpringerLink
Log in

Logarithmic growth of the Bergman Kernel for weakly pseudoconvex domains in ℂ3 of finite type

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

Abstract

If G⊂⊂ℂnis pseudoconvex with smooth boundary and zo∈bG is a point_of finite type, one can ask the question: Does the Bergman kernel KG(z,¯z) grow like a rational power of dist(z,bG) when z approaches zo nontangentially? This question is suggested by observations for the domains Upg defined below. But the answer to this question is in general negative as is shown by a counterexample in ℂ3.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. D'ANGELO, J.P.: A note on the Bergman kernel. Duke Math. Journal45,2 (1978) 259–265

    Google Scholar 

  2. D'ANGELO, J.P.: Real hypersurfaces, order of contact, and applications. Ann. of Math.115 (1982) 615–637

    Google Scholar 

  3. BEDFORD, E.- FORNAESS, J.E.: Biholomorpnic maps of weakly pseudoconvex domains. Duke Math.Journal45 (1978) 711–719

    Google Scholar 

  4. BERGMAN, S.: The kernel function and conformal mapping. AMS-Survey¯V, 2ndEdition, Providence R.I. (1970)

  5. BONAMI, A. -LOHUÉ, N.: Projecteurs de Bergman et de Szegö pour une classe des domaines faiblement pseudoconvexes et estimations Lp. Prepublication Université de Paris-Sud.

  6. CATLIN, D.: Invariant metrics on pseudoconvex domains. Preprint

  7. DIEDERICH, K.: Das Randverhalten der Bergmanschen Kernfunktion und Metrik in streng pseudokonvexen Gebieten. Math.Annalen187 (1970) 9–36

    Google Scholar 

  8. DIEDERICH, K. - FORNAESS, J.E. - HERBORT, G.: Boundary behavior of the Bergman metric. Proc.of Symposia in Pure Mathem., AMS, Providence, to appear

  9. KOHN, J.J.: Boundary behavior of\(\bar \partial \) on weakly pseudoconvex manifolds of dimension two. J.Diff.Geometry6 (1972) 523–542

    Google Scholar 

  10. OHSAWA, T.: Boundary behavior of the Bergman kernel function on pseudoconvex domains. To appear in Publ. of R.I.M.S. Kyoto University (1981)

Download references

Author information

Authors and Affiliations

  1. Fachbereich 7-Mathematik, Universität-Gesamthochschule Wuppertal, Gaußstraße 20, 5600, Wuppertal 1, Germany

    Gregor Herbort

Authors
  1. Gregor Herbort
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Herbort, G. Logarithmic growth of the Bergman Kernel for weakly pseudoconvex domains in ℂ3 of finite type. Manuscripta Math 45, 69–76 (1983). https://doi.org/10.1007/BF01168581

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01168581

Keywords

Search

Navigation