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

TL;DR

This paper investigates -biLipschitz mappings in quasiconvex metric spaces, providing characterizations and demonstrating that locally quasisymmetric equivalences are quasimb4bius, thus deepening understanding of geometric mappings.

Contribution

It introduces new characterizations of -biLipschitz mappings and links local quasisymmetry to quasimb4bius mappings in uniform metric spaces.

Findings

Characterizations of -biLipschitz mappings in quasiconvex spaces

Proof that local quasisymmetry implies quasimb4bius equivalence

Quantitative relations between different classes of mappings

Abstract

This paper focuses on properties of \partial-biLipschitz mappings which were recently introduced by Bulter. We establish several characterizations for the class of \partial-biLipschitz mappings between domains in quasiconvex metric spaces. As an application, we show that a locally quasisymmetric equivalence between uniform metric spaces is quasim\"obius, quantitatively.