Weakly Quasisymmetric Maps and Uniform Spaces



: Li YX, Vuorinen M, Zhou QS

Publisher: SPRINGER HEIDELBERG

: 2018

: Computational Methods and Function Theory

: COMPUTATIONAL METHODS AND FUNCTION THEORY

: COMPUT METH FUNCT TH

: 18

: 4

: 689

: 715

: 27

: 1617-9447

DOI: https://doi.org/10.1007/s40315-018-0248-0

: https://arxiv.org/abs/1705.05671


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.



Last updated on 2024-26-11 at 13:02