Planar Bilipschitz Extension from Separated Nets

Michael Dymond, Vojtěch Kaluža

We prove that every $L$-bilipschitz mapping ${\mathbb{Z}}^2\to {\mathbb{R}}^2$ can be extended to a $C(L)$-bilipschitz mapping ${\mathbb{R}}^2\to {\mathbb{R}}^2$ and provide a polynomial upp…