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Estimation of the Carathéodory distance on pseudoconvex domains of finite type whose boundary has Levi form of corank at most one

Volume 109 / 2013

Gregor Herbort Annales Polonici Mathematici 109 (2013), 209-260 MSC: Primary 32F45; Secondary 32T25, 32T45. DOI: 10.4064/ap109-3-1

Abstract

We study the class of smooth bounded weakly pseudoconvex domains $D\subset \mathbb C^n$ whose boundary points are of finite type (in the sense of J. Kohn) and whose Levi form has at most one degenerate eigenvalue at each boundary point, and prove effective estimates on the invariant distance of Carathéodory. This completes the author's investigations on invariant differential metrics of Carathéodory, Bergman, and Kobayashi in the corank one situation and on invariant distances on pseudoconvex finite type domains in dimension two.

Authors

  • Gregor HerbortFachbereich Mathematik und Naturwissenschaften
    Bergische Universität Wuppertal
    D-42097 Wuppertal, Germany
    e-mail

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