Champagne subregions of the disk whose bubbles carry harmonic measure
type: Item
instance of: scholarly article
title: Champagne subregions of the disk whose bubbles carry harmonic measure
zbMATH Open document ID: 1006.30019
author: John R. Akeroyd
published in: Mathematische Annalen
publication date: 2002-09-17T00:00:00Z
review text: Let \(G\) be a region in the unit dik \(D\) such that the boundary of the unbounded component of \(\mathbb{C}\setminus\overline G\) is the unit circle \(\partial\mathbb{D}\). It is proved that for any \(\varepsilon> 0\) there exists a sequence \(\{\Delta_n\}\) of pairwise disjoint closed disks in \(G\) whose set of accumulation points coincides with \(\partial\mathbb{D}\), the sum of the radii is less than \(\varepsilon\), and the harmonic measure of \(\mathbb{D}\setminus\bigcup_n \Delta_n\) does not charge \(\partial\mathbb{D}\).
Mathematics Subject Classification ID: 30C85
Mathematics Subject Classification ID: 31A15
Mathematics Subject Classification ID: 30D55
Mathematics Subject Classification ID: 30E10
Mathematics Subject Classification ID: 46E15
zbMATH DE Number: 1801552
zbMATH Keywords: harmonic measure
MaRDI profile type: Publication
full work available at URL: s002080100303
OpenAlex ID: W2008932756
DOI: 10.1007/S002080100303
description: scientific article; zbMATH DE number 1801552