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Optimal extension of Lipschitz embeddings in the plane

Optimal extension of Lipschitz embeddings in the plane 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Wiley

Optimal extension of Lipschitz embeddings in the plane

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References (28)

Publisher
Wiley
Copyright
© 2019 London Mathematical Society
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/blms.12255
Publisher site
See Article on Publisher Site

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.

Journal

Bulletin of the London Mathematical SocietyWiley

Published: Aug 1, 2019

Keywords: ; ; ;

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