Quasisymmetric extension on the real line

Vellis, Vyron

doi:10.1090/proc/13346

Quasisymmetric extension on the real line
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Proc. Amer. Math. Soc. 146 (2018), 2435-2450 Request permission

Abstract:

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

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