A criterion for quasi-simple plane curves
type: Item
instance of: scholarly article
title: A criterion for quasi-simple plane curves
zbMATH Open document ID: 1043.30003
DOI: 10.1007/BF03321022
author: Caren N. Genthner
author: Stephan Ruscheweyh
author: Luis Salinas
published in: Computational Methods and Function Theory
publication date: 2003-10-22T00:00:00Z
review text: An oriented closed curve \(\gamma\) in the complex \(\mathbb{C}\) is called quasi-simple if it represents the positive oriented boundary of a simply connected domain \(D\subset\mathbb{C}\). In the paper, a non-standard criterion for closed curves to be quasi-simple is given. Roughly speaking, the main result asserts that a sufficient condition is a possibility to decompose the curve such that the arcs are quasi-simple and the vertexes are attainable from \(\infty\). In the case of piecewise smooth curve conditions on the arcs are formulated in terms of behavior of normal vector. These results are used to establish the univalence of the extremal polynomials in the maximal range problem for simply connected domains.
Mathematics Subject Classification ID: 30C10
Mathematics Subject Classification ID: 30C55
zbMATH DE Number: 1995507
zbMATH Keywords: univalence of the extremal polynomials
zbMATH Keywords: piecewise close-to-convex simple curves
reviewed by: V. V. Goryainov
MaRDI profile type: Publication
cites work: On maximal ranges of polynomial spaces in the unit disk
cites work: On maximal polynomial ranges in circular domains
full work available at URL: https://doi.org/10.1007/bf03321022
OpenAlex ID: W2054791173
description: scientific article; zbMATH DE number 1995507