A1 Refereed original research article in a scientific journal
Weakly Quasisymmetric Maps and Uniform Spaces
Authors: Li YX, Vuorinen M, Zhou QS
Publisher: SPRINGER HEIDELBERG
Publication year: 2018
Journal: Computational Methods and Function Theory
Journal name in source: COMPUTATIONAL METHODS AND FUNCTION THEORY
Journal acronym: COMPUT METH FUNCT TH
Volume: 18
Issue: 4
First page : 689
Last page: 715
Number of pages: 27
ISSN: 1617-9447
DOI: https://doi.org/10.1007/s40315-018-0248-0
Self-archived copy’s web address: https://arxiv.org/abs/1705.05671
Abstract
Suppose that X and Y are quasiconvex and complete metric spaces, that is a homeomorphism. In this paper, we first give some basic properties of short arcs, and then we show that if f is a weakly quasisymmetric mapping and is a quasiconvex domain, then the image f(D) of every uniform subdomain D in G is uniform. As an application, we get t is a uniform domain, then the images of the short arcs in G under f are uniform arcs in the sense of diameter.
Suppose that X and Y are quasiconvex and complete metric spaces, that is a homeomorphism. In this paper, we first give some basic properties of short arcs, and then we show that if f is a weakly quasisymmetric mapping and is a quasiconvex domain, then the image f(D) of every uniform subdomain D in G is uniform. As an application, we get t is a uniform domain, then the images of the short arcs in G under f are uniform arcs in the sense of diameter.
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