Sets of constant distance from a Jordan curve

Vyron Vellis, Jang Mei Wu

Research output: Contribution to journalArticlepeer-review


We study the ε-level sets of the signed distance function to a planar Jordan curve γ, and ask what properties of γ ensure that the ε-level sets are Jordan curves, or uniform quasicircles, or uniform chord-arc curves for all sufficiently small ε. Sufficient conditions are given in term of a scaled invariant parameter for measuring the local deviation of subarcs from their chords. The chordal conditions given are sharp.

Original languageEnglish (US)
Pages (from-to)211-230
Number of pages20
JournalAnnales Academiae Scientiarum Fennicae Mathematica
Issue number1
StatePublished - 2014


  • Chordal property
  • Chordarc curves
  • Distance function
  • Jordan curves
  • Level sets
  • Quasicircles

ASJC Scopus subject areas

  • General Mathematics


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