Peak curves in weakly pseudoconvex boundaries in C2 |
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Authors: | L. Boutet de Monvel A. Iordan |
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Affiliation: | (1) Institut de Mathématiques, UMR 9994 du CNRS, Université de Paris 6, Tour 46-0, 5-ième étage, boite 172, 4 place Jussieu, F-75252 Paris Cedex 05, France |
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Abstract: | LetD be a pseudoconvex domain with real analytic boundary in C2. A subsetE of ∂D is a local peak set for if for everyp ∈ ∂D, there exist a neighborhoodU ofp and a holomorphic functionf onU such thatf = 1 onE∩U and |f| < 1 on . 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. |
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Keywords: | KeywordHeading" >Math Subject Classification 32E25 32F15 32F25 |
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