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

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 quasimöbius, quantitatively.

17 pages; To appear in Bulletin des sciences mathématiques