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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.
Bulletin of the London Mathematical Society – Wiley
Published: Aug 1, 2019
Keywords: ; ; ;
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