Peak curves in weakly pseudoconvex boundaries in \(\mathbb{C}^2\)
type: Item
instance of: scholarly article
title: Peak curves in weakly pseudoconvex boundaries in \(\mathbb{C}^2\)
zbMATH Open document ID: 0916.32014
DOI: 10.1007/BF02921702
author: Andrei Iordan
author: Louis Boutet de Monvel
published in: The Journal of Geometric Analysis
publication date: 1999-07-19T00:00:00Z
review text: Let \(D\) be a weakly pseudoconvex domain with real analytic boundary of finite type in \(\mathbb{C}^2\), and let \({\mathcal O}(\overline D)\) be the algebra of holomorphic functions in a neighborhood of \(D\). In this paper a necessary and a sufficient condition are given in order to provide the existence of real analytic curves passing through a point \(p\in\partial D\), which are local peak sets for \({\mathcal O}(\overline D)\). Also the authors explicitly exhibit domains \(D\subset\mathbb{C}^2\) with real analytic boundary and a point \(p\in \partial D\) which is a local peak point for \({\mathcal O}(\overline D)\); yet there are no real analytic curves through \(p\) that are local peak sets for \({\mathcal O}(\overline D)\).
reviewed by: Tan Vovan
Mathematics Subject Classification ID: 32A38
Mathematics Subject Classification ID: 32T99
Mathematics Subject Classification ID: 32V40
zbMATH DE Number: 1192501
zbMATH Keywords: weakly pseudoconvex boundaries
zbMATH Keywords: algebra of holomorphic functions
zbMATH Keywords: local peak sets
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1192501