@article{Qu2022, 
author = {Feifei Qu and Xin Wei},
title = {Limit behaviour of constant distance boundaries of Jordan curves},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {6},
pages = {11311-11319},
keywords = {constant distance boundary, Hausdorff distance, Jordan curve},
url = {https://www.sciopen.com/article/10.3934/math.2022631},
doi = {10.3934/math.2022631},
abstract = {For a Jordan curve    Γ in the complex plane, its constant distance boundary        Γ    λ   is an inflated version of    Γ. A flatness condition,    (  1      /    2  ,      r    0    )-chordal property, guarantees that        Γ    λ   is a Jordan curve when    λ is not too large. We prove that        Γ    λ   converges to    Γ, as    λ approaching to    0, in the sense of Hausdorff distance if    Γ has the    (  1      /    2  ,      r    0    )-chordal property.}
}