Plane sets allowing bilipschitz extensions - Alestalo, P.; Trotsenko, D. A. (MATHEMATICA SCANDINAVICA, 2009)
We give a geometric characterization for a plane set $A\subset {\mathsf R}^2$ to have the following linear bilipschitz extension property: For $0\le ε \le δ$, every $(1 + ε)$-bilipschitz map $f\colon A→ {\mathsf R}^2$ has a $(1 + Cε)$-bilipschitz extension to the whole plane ${\mathsf R}^2$.