Sets of constant distance from a Jordan curve

Vyron Vellis; Jang Mei Wu

doi:10.5186/aasfm.2014.3905

Sets of constant distance from a Jordan curve

Vyron Vellis, Jang Mei Wu

Research output: Contribution to journal › Article › peer-review

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	https://doi.org/10.5186/aasfm.2014.3905
State	Published - 2014
Externally published	Yes

Keywords

Chordal property
Chordarc curves
Distance function
Jordan curves
Level sets
Quasicircles

ASJC Scopus subject areas

Mathematics(all)

Online availability

10.5186/aasfm.2014.3905

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KW - Level sets

KW - Quasicircles

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Sets of constant distance from a Jordan curve

Abstract

Keywords

ASJC Scopus subject areas

Online availability

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