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Research Article | Open Access

Limit behaviour of constant distance boundaries of Jordan curves

Feifei Qu1, Xin Wei2( )
School of Science, Tianjin University of Technology and Education, Tianjin, 300222, China
School of Science, Xi'an Shiyou University, Xi'an, 710065, China
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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.

Keywords

constant distance boundaryHausdorff distanceJordan curve
CLC number: 53A04, 57N40

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AIMS Mathematics
Volume 7 Issue 6,
June 2022
Pages 11311-11319
DOI: 10.3934/math.2022631

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Cite this article:
Qu F, Wei X. Limit behaviour of constant distance boundaries of Jordan curves. AIMS Mathematics, 2022, 7(6): 11311-11319. https://doi.org/10.3934/math.2022631

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Received: 26 September 2021
Revised: 22 March 2022
Accepted: 25 March 2022
Published: 15 June 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)