Sets of constant distance from a Jordan curve

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 \(\epsilon\). Suf...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2013-11
Main Authors: Vellis, Vyron, Jang-Mei, Wu
Format: Article
Language:English
Subjects:
Chords (geometry)
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1311.2104