21 research outputs found
Sets of constant distance from a Jordan curve
We study the -level sets of the signed distance function to a
planar Jordan curve , and ask what properties of ensure that
the -level sets are Jordan curves, or uniform quasicircles, or
uniform chord-arc curves for all sufficiently small . 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