Geodesic
Large disks touching three sides of a quadrilateral
Alex Rodriguez1
1Stony Brook University, Department of Mathematics
Annales Fennici Mathematici, Tome 49 (2024) no. 2, p. 795–802

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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.
DOI : 10.54330/afm.154981
Keywords: Complex analysis, quasiconformal mappings in the plane

Alex Rodriguez  1

1 Stony Brook University, Department of Mathematics 
Alex Rodriguez. Large disks touching three sides of a quadrilateral. Annales Fennici Mathematici, Tome 49 (2024) no. 2, p. 795–802. doi: 10.54330/afm.154981
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