The Journal of Geometric Analysis

, Volume 7, Issue 1, pp 1–15 | Cite as

Peak curves in weakly pseudoconvex boundaries in C2

  • L. Boutet de Monvel
  • A. Iordan
Article
Received:

Abstract

LetD be a pseudoconvex domain with real analytic boundary in C2. A subsetE of ∂D is a local peak set for
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if for everyp ∈ ∂D, there exist a neighborhoodU ofp and a holomorphic functionf onU such thatf = 1 onE∩U and ¦f¦ < 1 on\(\bar D \cap U\backslash E\). We give conditions for the existence of real analytic LPι curves in ∂D through a point of finite type.

On the other hand, we give examples showing that: (a) there exist a domainD and a real analytic curve γ in ∂D such that the complexification of γ intersectsD only along γ, but γ is not LPι, and (b) there exist a domain D and a pointp ∈ ∂D, which is LPι, of finite type, but such that ∂D contains no real analytic LP∂ curve throughp.

Math Subject Classification

32E25 32F15 32F25 

Key Words and Phrases

complex-tangential finite type peak set pseudoconvex domain 
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Copyright information

© Mathematica Josephina, Inc. 1997

Authors and Affiliations

  • L. Boutet de Monvel
    • 1
  • A. Iordan
    • 1
  1. 1.Institut de Mathématiques, UMR 9994 du CNRSUniversité de Paris 6Paris Cedex 05France

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