Isoperimetric inequalities for capacities in the plane
type: Item
instance of: scholarly article
title: Isoperimetric inequalities for capacities in the plane
zbMATH Open document ID: 0739.31001
DOI: 10.1007/BF01444617
author: S. Singh
published in: Mathematische Annalen
publication date: 1992-09-26T00:00:00Z
full work available at URL: https://eudml.org/doc/164910
review text: Let \(d=d_ e(K)\) denote the exterior deficiency of a connected compact set \(K\) in the complex plane with strictly positive area and connected complement \((d_ e(K)=r_ e(K)/r_ 0(G)-1\), \(r_ e(K)\) exterior radius of \(K\), \(r_ 0(K)\) radius of a disk \(K_ 0\) having the same area as \(K\)). It is shown that, for every \(c>1/2\), \[ \hbox{Cap} K\geq (1+c(d^ 2/\ln(1/d)))\hbox{Cap} K_ 0 \] if \(d\) is sufficiently small. Examples of starlike sets are given where the converse inequality holds for every \(c>1\).
Mathematics Subject Classification ID: 31A15
Mathematics Subject Classification ID: 30C85
zbMATH DE Number: 56278
zbMATH Keywords: connected compact set
zbMATH Keywords: starlike sets
reviewed by: Wolfhard Hansen
MaRDI profile type: Publication
cites work: Q5574105
cites work: Isoperimetric inequalities in potential theory
cites work: Q4026542
OpenAlex ID: W2091534325
description: scientific article; zbMATH DE number 56278