Polynomially convex hulls of unions of real planes in \({\mathbb C}^ n\)
type: Item
instance of: scholarly article
title: Polynomially convex hulls of unions of real planes in \({\mathbb C}^ n\)
zbMATH Open document ID: 0688.32014
author: Pascal J. Thomas
publication date: 1990-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/74881
review text: Building on the work of \textit{B. Weinstock} [Math. Ann. 282, No. 1, 131--138 (1988; Zbl 0628.32015)] about the union of two subspaces, we show that \({\mathbb C}^ n\) can be obtained as the polynomially convex hull of a finite union of maximal totally real vector subspaces for any n greater than one. This is in sharp contrast with the fact that it takes a set of positive capacity of complex lines in \({\mathbb C}^ 2\) to obtain the whole space as hull. The special case of three real planes of \({\mathbb C}^ 2\) is studied: if the three pairwise unions are not polygonally convex, the hull contains an open cone but is smaller than \({\mathbb C}^ 2\).
reviewed by: Pascal J. Thomas
Mathematics Subject Classification ID: 32E20
zbMATH DE Number: 4127602
zbMATH Keywords: polynomial hulls
zbMATH Keywords: totally real subspace
zbMATH Keywords: approximation theory
MaRDI profile type: Publication
OpenAlex ID: W2313051720
cites work: Stability of Polynomial Convexity of Totally Real Sets
cites work: Q5517147
cites work: Normal forms for real surfaces in \(C^ 2\) near tangents and hyperbolic surface transformations
cites work: Q3346564
cites work: Q3887749
cites work: Totally real imbeddings and the universal covering spaces of domains of holomorphy: Some examples
cites work: On the polynomial convexity of the union of two maximal totally real subspaces of \(\mathbb C^n\)
DOI: 10.5802/AIF.1217
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 4127602