A nonremovable generic 4-ball in the unit sphere of \(\mathbb{C}^3\)
type: Item
instance of: scholarly article
title: A nonremovable generic 4-ball in the unit sphere of \(\mathbb{C}^3\)
zbMATH Open document ID: 0953.32009
DOI: 10.1215/S0012-7094-00-10213-X
published in: Duke Mathematical Journal
publication date: 2001-01-29T00:00:00Z
review text: A compact \(K\Subset S^{2n-1}\) in the unit sphere of \(\mathbb{C}^n\) is called removable if any continuous (but not necessarily bounded) function \(f\) on \(S^{2n-1}\setminus K\), which satisfies there the tangential Cauchy-Riemann equation \(\overline\partial_bf=0\), extends to an analytic function in the unit ball \(B^{2n}\). The main result of the paper is an example of the smooth generic 4-ball \(B^4\) in \(S^5\subset\mathbb{C}^3\) which is not removable. I.e. there exists an imbedding \(\varphi:B^4\to S^5\) such that the CR-dimension of \(\varphi (B^4)\) is one at every point and there exists an entire function \(f\) in \(\mathbb{C}^3\) such that its zero set \(X\) intersects \(S^5\) transversally and \(X\cap \overline B^6\subset \varphi(B^4)\).
Mathematics Subject Classification ID: 32D20
zbMATH DE Number: 1437629
zbMATH Keywords: generic manifold
zbMATH Keywords: removable set
author: Burglind Jöricke
author: Nikolay Shcherbina
reviewed by: S. Ivashkovich
MaRDI profile type: Publication
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full work available at URL: s0012-7094-00-10213-x
OpenAlex ID: W2086936099
description: scientific article; zbMATH DE number 1437629