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Geometric and analytic boundary invariants on pseudoconvex domains. Comparison results

  • K. Diederich
  • G. Herbort
Article

Abstract

We consider for smooth pseudoconvex bounded domains Ω ⊂ ℂn of finite type as local analytic invariants on the boundary the growth orders of the Bergman kernel and the Bergman metric and the best possible order of subellipticity ε1 > 0 for the\(\bar \partial - Neumann\) problem. Furthermore, we consider as local geometric invariants on ∂Ω the order of extendability, the exponent of extendability, the 1-type, and the multitype. Various new inequalities between these invariants are proved, giving in particular analytic information from geometric input. On the other hand, a careful consideration of several series of examples of such domains Ω shows that starting fromn ≥ 3 (essentially) each of these invariants is independent of the remaining ones.

Math Subject Classification

32F15 32H10 32H15 32F20 

Key Words and Phrases

Pseudoconvex domains Bergman kernel Bergman metric \(\bar \partial - Neumann\) problem finite type multitype pseudoconvex extendability 

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Copyright information

© Mathematica Josephina, Inc. 1993

Authors and Affiliations

  • K. Diederich
    • 1
  • G. Herbort
    • 1
  1. 1.Universität Wuppertal56 Wuppertal 1Germany

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