Planar rectangular sets and Steiner symmetrization
type: Item
instance of: scholarly article
title: Planar rectangular sets and Steiner symmetrization
zbMATH Open document ID: 0919.52008
author: Paul R. Scott
published in: Elemente der Mathematik
publication date: 1998-10-13T00:00:00Z
review text: The paper concerns (in fact) compact convex subsets of the Euclidean plane (though the author does not assume compactness). A set \(K\) is said to be rectangular with respect to a pair of orthogonal lines if no inscribed rectangle with sides parallel to those lines has exactly three of its vertices on the boundary of \(K\). Let \(S_L\) be the Steiner symmetrization with respect to a line \(L\). Theorem. \(K\) is rectangular with respect to \((L_1,L_2)\) if and only if \(S_{L_1} S_{L_2}(K)= S_{L_2} S_{L_1}(K)\).
Mathematics Subject Classification ID: 52A10
zbMATH DE Number: 1210209
zbMATH Keywords: convex subset of \(\mathbb{R}^2\)
zbMATH Keywords: inscribed rectangle
zbMATH Keywords: Steiner symmetrization
reviewed by: Maria Moszyńska
MaRDI profile type: Publication
full work available at URL: s000170050030
OpenAlex ID: W2025889699
cites work: Q5508161
DOI: 10.1007/S000170050030
description: scientific article; zbMATH DE number 1210209