Quasihyperbolic mappings in length metric spaces

Abstract

In this paper, we discuss the local properties of quasihyperbolic mappings in metric spaces, which are related to an open problem raised by Huang et al in 2016. Our result is a partial solution to this problem, which is also a generalization of the corresponding result obtained by Huang et al in 2016.

A note on $\partial$-bilipschitz mappings in quasiconvex metric spaces

“…We investigate new characterizations of ∂-biLipschitz mappings between domains (open and connected nonempty subsets) in quasiconvex metric spaces. For more investigations concerning properties of quasiconformal mappings in this setting, one may refer [8][9][10]20].…”

“…The class of locally biLipschitz mappings mentioned in Theorem 1.4(4) was introduced by Bonk et al [1], where they demonstrated that there is a oneto-one correspondence between Gromov hyperbolic space category with biLipschitz mappings as morphisms and uniform space category with quasisimilarity mappings as morphisms. For more investigations about these mappings, see [18,20].…”

Bilipschitz mappings and quasihyperbolic mappings in real Banach spaces

“…The authors answered the problem under certain additional conditions. Our result, Theorem 1.1, in this paper shows that the related conditions in [4,8,9] cannot be removed.…”

“…Added information. After the acceptance of this paper, we found three related references, see [4,8,9]. The main aim of these papers is to investiage Väisälä's open problem discussed in this paper.…”