Optimal extension of Lipschitz embeddings in the plane

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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.

Original languageEnglish (US)
JournalBulletin of the London Mathematical Society
DOIs
StatePublished - Jan 1 2019

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Lipschitz
Lipschitz Map
Homeomorphism
Unit circle
Unit Disk
Circle

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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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.",
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