A1 Refereed original research article in a scientific journal
On the stability of φ-uniform domains [On the stability of phi-uniform domains]
Subtitle: [On the stability of phi-uniform domains]
Authors: R. Klén, Y. Li, S. K. Sahoo, M. Vuorinen
Publisher: Springer-Verlag Wien
Publishing place: WIEN; SACHSENPLATZ 4-6, PO BOX 89, A-1201 WIEN, AUSTRIA
Publication year: 2014
Journal: Monatshefte für Mathematik
Journal name in source: Monatshefte fur Mathematik
Journal acronym: Mon.heft.Math.
Volume: 174
Issue: 2
First page : 231
Last page: 258
Number of pages: 28
ISSN: 0026-9255
DOI: https://doi.org/10.1007/s00605-013-0576-0
Web address : http://api.elsevier.com/content/abstract/scopus_id:84900326202
We study two metrics, the quasihyperbolic metric and the distance ratio metric of a subdomain G ⊂ ℝ. In the sequel, we investigate a class of domains, so called φ-uniform domains, defined by the property that these two metrics are comparable with respect to a homeomorphism φ from [0,∞) to itself. Finally, we discuss a number of stability properties of φ-uniform domains. In particular, we show that the class of φ-uniform domains is stable in the sense that removal of a geometric sequence of points from a φ-uniform domain yields a φ-uniform domain. © 2013 Springer-Verlag Wien.
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