Analytic discs attached to a generating CR-manifold
type: Item
instance of: scholarly article
title: Analytic discs attached to a generating CR-manifold
zbMATH Open document ID: 0856.32012
DOI: 10.1007/BF02559708
published in: Arkiv för Matematik
publication date: 1996-08-05T00:00:00Z
review text: The author gives a complete finite-dimensional parametrization of perturbations by analytic discs with their boundaries kept in a generating CR-fibration \(\{M (\xi) \}_{\xi \in \partial D}\), \(M (\xi) \subset \mathbb{C}^{m + n}\) over the unit circle \(\partial D\), under the condition that the partial indices of the original path are all greater than or equal to \(-1\). Here CR-bundle means that each fiber is a real vector subspace of CR-dimension \(m\), and ``generating'' means that each fiber is a generating subspace of \(\mathbb{C}^{m + n}\). This is a generalization of results by Globevnik and other people (including the author himself) in case when the boundaries are kept in a maximal real submanifold of \(\mathbb{C}^n\), which corresponds to \(m = 0\) in the above. This problem has applications such as the determination of the polynomial hull or the extension of CR-functions. Some geometric properties of the perturbations are discussed, e.g. the dimension of the subspaces of cotangent vectors of the perturbations conormal to the original fibers is shown to be constant along the circle.
Mathematics Subject Classification ID: 32V05
Mathematics Subject Classification ID: 32V99
Mathematics Subject Classification ID: 32D10
Mathematics Subject Classification ID: 32C25
zbMATH DE Number: 894900
zbMATH Keywords: CR-manifold
zbMATH Keywords: analytic discs
zbMATH Keywords: CR-fibration
author: Miran Cerne
reviewed by: Akira Kaneko
MaRDI profile type: Publication
cites work: Hulls of Deformations in C n
cites work: Holomorphic extension of CR functions
cites work: Q5565773
cites work: Q3791451
cites work: Perturbation by analytic discs along maximal real submanifolds of \(C^ N\)
cites work: Pseudo holomorphic curves in symplectic manifolds
cites work: Q3924489
cites work: On the Reflection Principle in Several Complex Variables
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description: scientific article; zbMATH DE number 894900