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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
DOI: https://doi.org/10.1090/S1088-4173-2012-00243-3
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
Email: lvkovale@syr.edu

DOI: https://doi.org/10.1090/S1088-4173-2012-00243-3
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.

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