Perturbing analytic discs attached to maximal real submanifolds of \(\mathbb{C}^ N\)
type: Item
instance of: scholarly article
title: Perturbing analytic discs attached to maximal real submanifolds of \(\mathbb{C}^ N\)
zbMATH Open document ID: 0861.32013
DOI: 10.1016/0019-3577(96)88655-1
author: Josip Globevnik
published in: Indagationes Mathematicae. New Series
publication date: 1996-06-09T00:00:00Z
review text: Let \(f\) be an analytic disc in \(\mathbb{C}^N\) attached to a maximal real submanifold \(M\) of \(\mathbb{C}^N\). The author introduced in a recent paper [Math. Z. 217, No. 2, 287-316 (1994; Zbl 0806.58044)] partial indices \(k_j\), \(1\leq j\leq N\), of \(M\) along the boundary of \(f\) and showed that if \(k_j\geq 0\) for all \(j\) then the family of nearby analytic discs attached to \(M\) depends on \(k_1+ \cdots +k_N\) parameters. Y.-G. Oh sharpened this by proving the same when \(k_j\geq -1\) for all \(j\) and showed that in terms of stability this is the best possible condition. In the paper under review the author explains why the latter condition is natural and give a simple proof of Oh's result in the orientable case.
Mathematics Subject Classification ID: 32G10
Mathematics Subject Classification ID: 32V40
Mathematics Subject Classification ID: 32D10
zbMATH DE Number: 885620
zbMATH Keywords: analytic disc
zbMATH Keywords: maximal real submanifold
reviewed by: Viorel Vâjâitu
MaRDI profile type: Publication
full work available at URL: 0019-3577(96)88655-1
OpenAlex ID: W2060844071
cites work: On the geometry of analytic discs attached to real manifolds
cites work: Q5538494
cites work: REGULARITY OF THE BOUNDARIES OF ANALYTIC SETS
cites work: Analytic disks with boundaries in a maximal real submanifold of \({\mathbb C}^ 2\)
cites work: Perturbation by analytic discs along maximal real submanifolds of \(C^ N\)
cites work: Q4183573
cites work: Q3286812
cites work: Q3754832
cites work: Q5550638
description: scientific article; zbMATH DE number 885620