Bridged extremal distance and maximal capacity
type: Item
instance of: scholarly article
title: Bridged extremal distance and maximal capacity
zbMATH Open document ID: 0865.30031
author: Robert E. Thurman
published in: Pacific Journal of Mathematics
publication date: 1997-06-15T00:00:00Z
review text: We introduce the concept of ``bridged extremal distance'' between subsets \(X\) and \(Z\) lying on the boundary of a finitely-connected domain \(G\) -- that is, the extremal length of the family of curves connecting \(X\) and \(Z\) which are allowed to stop at a component of the ``bridge'' \(Y= \partial G\setminus (X \cup Z)\) and re-emerge from any other point of that component. We identify bridged extremal distance with the extremal problem of ``minimal extremal distance'', and express it in terms of the period matrix associated with the harmonic measures of the boundary components of \(G\). We then use bridged extremal distance to give an extremal length interpretation of ``maximal capacity'', via ``reduced extremal distance''.
Mathematics Subject Classification ID: 30C70
Mathematics Subject Classification ID: 30C20
zbMATH DE Number: 950230
zbMATH Keywords: conformal mapping
zbMATH Keywords: logarithmic capacity
zbMATH Keywords: multiply-connected domains
zbMATH Keywords: extremal length
zbMATH Keywords: extremal distance
zbMATH Keywords: extremal problem
zbMATH Keywords: harmonic measures
MaRDI profile type: Publication
full work available at URL: pjm.1996.176.507
OpenAlex ID: W1509015964
DOI: 10.2140/PJM.1996.176.507
description: scientific article; zbMATH DE number 950230