Characterization of removable sets in strongly pseudoconvex boundaries
type: Item
instance of: scholarly article
title: Characterization of removable sets in strongly pseudoconvex boundaries
zbMATH Open document ID: 0823.32004
DOI: 10.1007/BF02559581
author: Guido Lupacciolu
published in: Arkiv för Matematik
publication date: 1995-05-04T00:00:00Z
review text: Let \(D\) be a relatively compact domain in the complex manifold \(M\). A compact \(K \subset \partial D\) is called removable if \(\partial D \backslash K\) is \(C^ 1\)-smooth and every continuous \(CR\)-function \(f\) on \(\partial D \backslash K\) has a continuous extension \(F\) onto \(\overline D \backslash K\) which is holomorphic on \(D\). The main result of the paper is the following Theorem 1. Let \(M\) be a Stein manifold and \(D \Subset M\) be a \(C^ 2\)- smooth strictly pseudoconvex domain such that \(\overline D\) is \({\mathcal O} (M)\)-convex. Then for a compact \(K \subset \partial D\) the following two conditions are equivalent: (a) \(K\) is removable; (b) The restriction map \(Z^{n,n - 2}_{\overline \partial} (M) \to Z_{\overline \partial}^{n,n - 2} (K)\) has a dense image and \(H^{n,n - 2}_{\overline \partial} (K) = 0\). Here \(Z_{\overline \partial}^{n,n - 2} (K)\) is equipped with a locally convex inductive limit topology.
Mathematics Subject Classification ID: 32D20
Mathematics Subject Classification ID: 32D15
zbMATH DE Number: 750859
zbMATH Keywords: removable sets
zbMATH Keywords: strongly pseudoconvex boundary
zbMATH Keywords: holomorphic extension
reviewed by: S. Ivashkovich
MaRDI profile type: Publication
cites work: A note on Hulls
cites work: Q4405461
cites work: Q4161581
cites work: A new class of polynomially convex sets
cites work: Q5183990
cites work: On boundaries of complex analytic varieties. I
cites work: Compact Holomorphically Convex Subsets of a Stein Manifold
cites work: Some Global Results on Extension of CR-Objects in Complex Manifolds
cites work: Topological Properties of q-Convex Sets
cites work: Complements of domains with respect to hulls of outside compact sets
cites work: Rado's Theorem for CR-Functions
cites work: Un théorème de dualité
cites work: Q4694622
cites work: Continuous Boundary Values of Analytic Functions of Several Complex Variables
description: scientific article; zbMATH DE number 750859