Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 39, 2014, 211-230

SETS OF CONSTANT DISTANCE FROM A JORDAN CURVE

Vyron Vellis and Jang-Mei Wu

University of Illinois, Department of Mathematics
1409 West Green Street, Urbana, IL 61820, U.S.A.; vellis1 'at' illinois.edu

University of Illinois, Department of Mathematics
1409 West Green Street, Urbana, IL 61820, U.S.A.; wu 'at' math.uiuc.edu

Abstract. 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.

2010 Mathematics Subject Classification: Primary 30C62; Secondary 57N40.

Key words: Chordal property, Jordan curves, distance function, level sets, quasicircles, chord-arc curves.

Reference to this article: V. Vellis and J.-M. Wu: Sets of constant distance from a Jordan curve. Ann. Acad. Sci. Fenn. Math. 39 (2014), 211-230.

Full document as PDF file

doi:10.5186/aasfm.2014.3905