Symmetrization and extension of planar bi-Lipschitz maps

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1 Scopus citations


We show that every centrally symmetric bi-Lipschitz embedding of the circle into the plane can be extended to a global bi-Lipschitz map of the plane with linear bounds on the distortion. This answers a question of Daneri and Pratelli in the special case of centrally symmetric maps. For general bi-Lipschitz embeddings our distortion bound has a combination of linear and cubic growth, which improves on the prior results. The proof involves a symmetrization result for bi-Lipschitz maps which may be of independent interest.

Original languageEnglish (US)
Pages (from-to)541-556
Number of pages16
JournalAnnales Academiae Scientiarum Fennicae Mathematica
StatePublished - 2018


  • Bi-Lipschitz extension
  • Conformal map
  • Harmonic measure

ASJC Scopus subject areas

  • General Mathematics


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