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