Weakly Quasisymmetric Maps and Uniform Spaces

摘要

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.