Quasisymmetric extension on the real line

Abstract

We give a geometric characterization of the sets $E\subset \mathbb{R}$ that satisfy the following property: every quasisymmetric embedding $f:E\to {\mathbb{R}}^n$ extends to a quasisymmetric embedding $f:\mathbb{R}\to {\mathbb{R}}^N$ for some $N\ge n$.

arXiv comment15 pages; to appear in the Proc. Amer. Math. Soc