Optimal extension of Lipschitz embeddings in the plane

Leonid V. Kovalev

doi:10.1112/blms.12255

Optimal extension of Lipschitz embeddings in the plane

Leonid V. Kovalev

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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 language	English (US)
Pages (from-to)	622-632
Number of pages	11
Journal	Bulletin of the London Mathematical Society
Volume	51
Issue number	4
DOIs	https://doi.org/10.1112/blms.12255
State	Published - Aug 1 2019

Keywords

26B35
30C35 (primary)
30L05
31A15 (secondary)

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1112/blms.12255

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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AB - 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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KW - 30C35 (primary)

KW - 30L05

KW - 31A15 (secondary)

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Optimal extension of Lipschitz embeddings in the plane

Abstract

Keywords

ASJC Scopus subject areas

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