Estimates for the Bergman kernel and metric of convex domains in ${\Bbb C}^n$

Volume 81 / 2003

Nikolai Nikolov, Peter Pflug Annales Polonici Mathematici 81 (2003), 73-78 MSC: Primary 32A25. DOI: 10.4064/ap81-1-6


Sharp geometrical lower and upper estimates are obtained for the Bergman kernel on the diagonal of a convex domain $D\subset {{\mathbb C}}^n$ which does not contain complex lines. It is also proved that the ratio of the Bergman and Carathéodory metrics of $D$ does not exceed a constant depending only on $n$.


  • Nikolai NikolovInstitute of Mathematics and Informatics
    Bulgarian Academy of Sciences
    1113 Sofia, Bulgaria
  • Peter PflugFachbereich Mathematik
    Carl von Ossietzky Universität Oldenburg
    Postfach 2503
    D-26111 Oldenburg, Germany

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