Analytic discs attached to conormal bundles of CR-manifolds
type: Item
instance of: scholarly article
title: Analytic discs attached to conormal bundles of CR-manifolds
zbMATH Open document ID: 0886.32008
author: Giuseppe Zampieri
published in: Advances in Mathematics
publication date: 1998-04-19T00:00:00Z
review text: For a pseudoconvex hypersurface \(M\) in \({\mathbb{C}}^n\), small analytic discs attached to \(M\) are in fact contained in \(M\) [see also \textit{K. Diederich} and \textit{J. E. Fornaess}, Invent. Math. 39, 129-141 (1977; Zbl 0353.32025)]. The author generalizes this result, namely: If \(M\) is a CR-submanifold of \( X= {\mathbb{C}}^n\), if \(z_0\in M\), if we consider a small analytic disc \(A\) (\(C^1\) up to the boundary ) attached to \(M\) through \( z_{0} \), if \(p_{0}\) is a point in the conormal bundle to \(M\) in \(X\) (minus the zero element) (=: \(T\)) whose image through the canonical projection is \( z_{0} \), if there exists a lift \(A^{\star}\) of \(A\) attached to \(T\) through \( p_{0} \) and if the Levi-form of \(M\) has a constant number of negative eigenvalues in a neighbourhood of \(p_{0}\), then, in fact, \(A \sqsubset M\) and \(A^{\star}\) is contained in \(T\).
Mathematics Subject Classification ID: 32V05
Mathematics Subject Classification ID: 32V99
Mathematics Subject Classification ID: 32U05
Mathematics Subject Classification ID: 32F10
Mathematics Subject Classification ID: 32T99
Mathematics Subject Classification ID: 53C15
zbMATH DE Number: 1044220
zbMATH Keywords: CR-manifolds
zbMATH Keywords: analytic discs
zbMATH Keywords: conormal bundle
reviewed by: Eugen Pascu
MaRDI profile type: Publication
full work available at URL: aima.1997.1636
OpenAlex ID: W2084568446
cites work: Q4000245
cites work: Complex manifolds in pseudoconvex boundaries
cites work: On the geometry of analytic discs attached to real manifolds
cites work: Pseudoconvex domains: bounded strictly plurisubharmonic exhaustion functions
cites work: Q3717382
cites work: Q1071902
cites work: Connections and propagation of analyticity for \(CR\) functions
cites work: Q4874430
cites work: Hypersurfaces through higher-codimensional submanifolds of \(\mathbb{C}^n\) with preserved Levi-kernel
DOI: 10.1006/AIMA.1997.1636
description: scientific article; zbMATH DE number 1044220