Open AccessLimit behaviour of constant distance boundaries of Jordan curves
Author(s) -
Feifei Qu,
Xin Wei
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022631
Subject(s) - lambda , mathematics , flatness (cosmology) , constant (computer programming) , boundary (topology) , combinatorics , limit (mathematics) , chordal graph , mathematical analysis , geometry , physics , astrophysics , computer science , optics , graph , cosmology , programming language
For a Jordan curve $ \Gamma $ in the complex plane, its constant distance boundary $ \Gamma_ \lambda $ is an inflated version of $ \Gamma $. A flatness condition, $ (1/2, r_0) $-chordal property, guarantees that $ \Gamma_ \lambda $ is a Jordan curve when $ \lambda $ is not too large. We prove that $ \Gamma_ \lambda $ converges to $ \Gamma $, as $ \lambda $ approaching to $ 0 $, in the sense of Hausdorff distance if $ \Gamma $ has the $ (1/2, r_0) $-chordal property.