Sharp distortion growth for bilipschitz extension of planar maps

Abstract

This note addresses the quantitative aspect of the bilipschitz extension problem. The main result states that any bilipschitz embedding of $\mathbb{R}$ into ${\mathbb{R}}^2$ can be extended to a bilipschitz self-map of ${\mathbb{R}}^2$ with a linear bound on the distortion.

arXiv comment9 pages. Slightly expanded introduction, added references

References in corpus (1)

• Radial extension of a bi-Lipschitz parametrization of a starlike Jordan curve

Cited by in corpus (1)

• Optimal extension of Lipschitz embeddings in the plane