The maximum of the conformal radius in the families of domains satisfying additional conditions
type: Item
instance of: scholarly article
title: The maximum of the conformal radius in the families of domains satisfying additional conditions
zbMATH Open document ID: 0907.30025
DOI: 10.1007/BF02358535
author: E. G. Emel'yanov
published in: Journal of Mathematical Sciences (New York)
publication date: 1998-10-12T00:00:00Z
full work available at URL: https://eudml.org/doc/68634
review text: Let \(R(D,a)\) denote the conformal radius of the simply connected domain \(D\) with respect to the point \(a\in D\). Let \(D(R_0)\) denote the set of all simply connected domains \(D\) in the complex plane with \(0,1\in D\) and for which \(R(D,0)\) has the prescribed value \(R_0\). The author poses and solves the problem of finding, in the set \(D(R_0)\), the domain \(D\) for which the conformal radius \(R(D,1)\) has the greatest value. The author then poses and solves the analogous problem for doubly connected domains. (For a doubly connected domain \(D\) with \(a\in D\), one needs to work with simply connected domains \(\widetilde D\subset D\), \(a\in \widetilde D.)\) Quadratic differentials and extremal decompositions play an important part in the proofs.
reviewed by: Renate McLaughlin
Mathematics Subject Classification ID: 30C75
zbMATH DE Number: 1107886
zbMATH Keywords: extremal metric
zbMATH Keywords: modulus
zbMATH Keywords: quadratic differentials
MaRDI profile type: Publication
cites work: Q3729303
cites work: Symmetrization in the geometric theory of functions of a complex variable
description: scientific article; zbMATH DE number 1107886