We give a geometric characterization of the sets $E\subset \mathbb{R}$ that satisfy the following property: every monotone quasisymmetric mapping $f: E \to \mathbb{R}$ extends to a quasisymmetric mapping $f:\mathbb{R}\to\mathbb{R}$.
Double Bubbles on the Real Line with Log-Convex Density
Isometric study of Wasserstein spaces --- the real line
A Note on Self-extremal Sets in $L_p(\Om)$ Spaces
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