Decomposition and removability properties of John domains
type: Item
instance of: scholarly article
title: Decomposition and removability properties of John domains
zbMATH Open document ID: 1157.30017
author: B. E. Eshmatov
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 2008-10-21T00:00:00Z
review text: A domain \(D\) is a \(c\)--John domain if for all points \(z_1, z_2 \in D\) there is a rectifiable curve \(\alpha \subset D\) joining them and \(\min_{j = 1,2} l(\alpha[z_j,z]) \leq c\, dist(z, \partial D)\) for each \(z \in \alpha\), [see \textit{O. Martio, J. Sarvas}, Ann. Acad. Sci. Fenn., Ser. A I 4, 383-401 (1979; Zbl 0406.30013)] for another definition. The domain \(D\) is said to have the John decomposition property if for some constant \(c\) each pair of points \(z_1, z_2 \in D\) is contained in a simply connected \(c\)--John domain which is included in \(D\). It is shown that \(D\) is a John domain iff it has the John decomposition property. In [\textit{O. Martio}, Rev. Roum. Math. Pures Appl. 33, No.1-2, 107-112 (1988; Zbl 0652.30012)] bilipschitz balls are used instead of John domains to prove a similar result. The authors also show that a removal of a finite number of points does not destroy the John property.
reviewed by: O. Martio
Mathematics Subject Classification ID: 30C65
zbMATH DE Number: 5354748
zbMATH Keywords: John domain
MaRDI profile type: Publication
full work available at URL: s12044-008-0028-2
OpenAlex ID: W1982833701
cites work: Q4379874
cites work: Quadrilaterals and John disks
cites work: Uniform domains and the ubiquitous quasidisk
cites work: Uniform domains and the quasi-hyperbolic metric
cites work: Q4439648
cites work: The Apollonian inner metric
cites work: Q3869782
cites work: Harmonic measure and hyperbolic distance in John disks
cites work: Injectivity theorems in plane and space
cites work: Quasiconformal and Bi-Lipschitz Homeomorphisms, Uniform Domains and the Quasihyperbolic Metric
cites work: John disks
cites work: Lectures on \(n\)-dimensional quasiconformal mappings
cites work: Uniform domains
cites work: Conformal geometry and quasiregular mappings
cites work: Q3593391
DOI: 10.1007/S12044-008-0028-2
description: scientific article; zbMATH DE number 5354748