, Volume 66, Issue 1, pp 85-115

Bi-lipschitz extensions in the plane

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Abstract

We show that a bi-Lipschitz mapF from a subset of a line or a circle into the plane can be extended to a bi-Lipschitz map of the whole plane onto itself, with the bi-Lipschitz constant depending only on that ofF.

This research was supported in part by NSF Grant DMS-9305792.