Quasisymmetric map

Summary

A quasisymmetric map is an embedding between metric spaces that distorts relative distances in a controlled way. It may stretch distances a lot, but it sends points in roughly the same relative position to points in roughly the same relative position. Quasisymmetric self-maps of the real line are the boundary values of quasiconformal maps of the upper half-plane. The notion makes sense in any metric space and is central in the analysis of quasiconformal maps on metric spaces.