Optimal extension of Lipschitz embeddings in the plane

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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)
Pages (from-to)622-632
Number of pages11
JournalBulletin of the London Mathematical Society
Issue number4
StatePublished - Aug 1 2019


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

ASJC Scopus subject areas

  • General Mathematics


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