On the structure of support points in the class \(\Sigma\)
type: Item
instance of: scholarly article
title: On the structure of support points in the class \(\Sigma\)
zbMATH Open document ID: 0612.30022
DOI: 10.1007/BF02796584
published in: Journal d'Analyse Mathématique
publication date: 1986-01-01T00:00:00Z
review text: The authors consider the family \(\Sigma\), continuous (complex-valued) linear functionals on it and elements of \(\Sigma\) for which a maximum of \({\mathcal R}L(f)\) occurs, called support points of L. Such an element maps \(\Delta\) : \(| z| >1\) onto a domain admissible with respect to the quadratic differential \[ Q(w)dw^ 2=L(1/(f-w))dw^ 2. \] The authors study the occurence of zeros of \(Q(w)dw^ 2\) on the complement \(\Gamma\) of f(\(\Delta)\). They conjecture that such zeros must be simple. This is not proven but it is shown that if \(\Gamma\) contains a zero of \(Q(w)dw^ 2\) of order at least two it cannot contain a set of two or more arcs emanating from this zero at equi-angular directions. The method is variational. Some further results are obtained in the case of second order zeros. It is shown that no such restrictive statements can be made about the order of zeros not on \(\Gamma\). Finally the authors discuss Ozawa numbers and a conjecture of Kirwan.
Mathematics Subject Classification ID: 30C70
Mathematics Subject Classification ID: 30F30
zbMATH DE Number: 3989722
zbMATH Keywords: support points
zbMATH Keywords: quadratic differential
zbMATH Keywords: Ozawa numbers
author: Yuk-J Leung
author: Glenn Schober
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02796584
OpenAlex ID: W4233884364
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description: scientific article; zbMATH DE number 3989722