Conformal Geometry and Dynamics

ISSN 1088-4173



Sharp distortion growth for bilipschitz extension of planar maps

Author: Leonid V. Kovalev
Journal: Conform. Geom. Dyn. 16 (2012), 124-131
MSC (2010): Primary 26B35; Secondary 57N35, 51F99, 54C25
Published electronically: April 18, 2012
MathSciNet review: 2910744
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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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Additional Information

Leonid V. Kovalev
Affiliation: Department of Mathematics, Syracuse University, Syracuse, New York 13244

Keywords: Bilipschitz extension, conformal map
Received by editor(s): March 15, 2012
Published electronically: April 18, 2012
Additional Notes: Supported by the NSF grant DMS-0968756.
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.