Abstract
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 language | English (US) |
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Pages (from-to) | 211-230 |
Number of pages | 20 |
Journal | Annales Academiae Scientiarum Fennicae Mathematica |
Volume | 39 |
Issue number | 1 |
DOIs | |
State | Published - 2014 |
Externally published | Yes |
Keywords
- Chordal property
- Chordarc curves
- Distance function
- Jordan curves
- Level sets
- Quasicircles
ASJC Scopus subject areas
- Mathematics(all)