Sets of constant distance from a Jordan curve

Vyron Vellis, Jang-Mei Wu
2014 Annales Academiae Scientiarum Fennicae: Mathematica  
We study the $\epsilon$-level sets of the signed distance function to a planar Jordan curve $\Gamma$, and ask what properties of $\Gamma$ ensure that the $\epsilon$-level sets are Jordan curves, or uniform quasicircles, or uniform chord-arc curves for all sufficiently small $\epsilon$. 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.
doi:10.5186/aasfm.2014.3905 fatcat:c73vcgpnjjhonokydol5kvl3iq