Sharp distortion growth for bilipschitz extension of planar maps

Kovalev, Leonid

doi:10.1090/S1088-4173-2012-00243-3

Sharp distortion growth for bilipschitz extension of planar maps
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by Leonid V. Kovalev PDF

Conform. Geom. Dyn. 16 (2012), 124-131 Request permission

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.

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