Mediatrix of two arcs of a quasicircle
type: Item
instance of: scholarly article
title: Mediatrix of two arcs of a quasicircle
zbMATH Open document ID: 0752.30015
DOI: 10.1007/BF02789204
published in: Journal d'Analyse Mathématique
publication date: 1992-06-25T00:00:00Z
review text: Given two nonempty disjoint closed subsets \(E\) and \(F\) of the plane, consider the set \(M\) of points in the plane at equal distance to \(E\) and \(F\). For example, if \(E\) and \(F\) are intervals on a line \(L\), then \(M\) is a line perpendicular to \(L\). It is natural to hope that \(M\) should have some special structure even for fairly general sets \(E\) and \(F\), and that \(M\) might be qualitatively similar to the simple example above under reasonable hypotheses on \(E\) and \(F\). Some results of this type are obtained in this paper, and in particular it is shown that \(M\) must be a chord-arc curve if \(E\) and \(F\) are two unbounded arcs of a quasicircle. One can ask analogous questions in higher dimensions, but one won't find any answers in this paper.
Mathematics Subject Classification ID: 30C99
Mathematics Subject Classification ID: 51M99
zbMATH DE Number: 9210
zbMATH Keywords: chord-arc curve
zbMATH Keywords: quasicircle
author: Guy David
author: Gaven J. Martin
author: Stephen Semmes
MaRDI profile type: Publication
cites work: Q5782967
cites work: Differentiation of integrals in \(\mathbb{R}^n\)
cites work: The quasihyperbolic metric and associated estimates on the hyperbolic metric
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description: scientific article; zbMATH DE number 9210