Large disks touching three sides of a quadrilateral

We show that every Jordan quadrilateral \(Q\subset\mathbb{C}\) contains a disk \(D\) so that \(\partial D\cap\partial Q\) contains points of three different sides of \(Q\). As a consequence, together with some modulus estimates from Lehto and Virtanen, we offer a short proof of the main result obtained by Chrontsios-Garitsis and Hinkkanen in 2024 and it also improves the bounds on their result.

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Publication Details

Journal
Annales Fennici Mathematici
Published
2024-12-18
DOI
https://doi.org/10.54330/afm.154981
Primary Topic
Advanced Theoretical and Applied Studies in Material Sciences and Geometry
Type
article
Field-Weighted Citation Impact
0.00

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article

Large disks touching three sides of a quadrilateral

Alex Rodriguez
Annales Fennici Mathematici
Advanced Theoretical and Applied Studies in Material Sciences and Geometry
article

Large disks touching three sides of a quadrilateral

Alex Rodriguez
article en

Abstract

We show that every Jordan quadrilateral \(Q\subset\mathbb{C}\) contains a disk \(D\) so that \(\partial D\cap\partial Q\) contains points of three different sides of \(Q\). As a consequence, together with some modulus estimates from Lehto and Virtanen, we offer a short proof of the main result obtained by Chrontsios-Garitsis and Hinkkanen in 2024 and it also improves the bounds on their result.

Annales Fennici MathematiciVol. 49(2)
Stony Brook University (US)
National Science Foundation
Openalex Percentile: Top 78%
Advanced Theoretical and Applied Studies in Material Sciences and Geometry
DOIOpen Access PDFOpenAlex
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Large disks touching three sides of a quadrilateral — Alex Rodriguez · Annales Fennici Mathematici (2024) | TGRS Research Map | TGRS