Optimal extension of Lipschitz embeddings in the plane

Abstract

We prove that every bi-Lipschitz embedding of the unit circle into the plane can be extended to a bi-Lipschitz map of the unit disk with linear bounds on the constants involved. This answers a question raised by Daneri and Pratelli. Furthermore, every Lipschitz embedding of the circle extends to a Lipschitz homeomorphism of the plane, again with a linear bound on the constant.

References in corpus (2)

• Sharp distortion growth for bilipschitz extension of planar maps
• Symmetrization and extension of planar bi-Lipschitz maps

Cited by in corpus (1)

• Planar Bilipschitz Extension from Separated Nets