Geodesic
A geometric property of quadrilaterals
Efstathios-Konstantinos Chrontsios-Garitsis1 ; Aimo Hinkkanen2
1University of Illinois Urbana-Champaign, Department of Mathematics, and University of Tennessee, Knoxville, Department of Mathematics
2University of Illinois Urbana-Champaign, Department of Mathematics
Annales Fennici Mathematici, Tome 49 (2024) no. 1, p. 281–302

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Quadrilaterals in the complex plane play a significant part in the theory of planar quasiconformal mappings. Motivated by the geometric definition of quasiconformality, we prove that every quadrilateral with modulus in an interval $[1/K, K]$, where $K>1$, contains a disk lying in its interior, of radius depending only on the internal distances between the pairs of opposite sides of the quadrilateral and on $K$.  
DOI : 10.54330/afm.145026
Keywords: Jordan domains, quadrilaterals, interior distances, quasiconformal mappings

Efstathios-Konstantinos Chrontsios-Garitsis  1   ; Aimo Hinkkanen  2

1 University of Illinois Urbana-Champaign, Department of Mathematics, and University of Tennessee, Knoxville, Department of Mathematics
2 University of Illinois Urbana-Champaign, Department of Mathematics 
Efstathios-Konstantinos Chrontsios-Garitsis; Aimo Hinkkanen. A geometric property of quadrilaterals. Annales Fennici Mathematici, Tome 49 (2024) no. 1, p. 281–302. doi: 10.54330/afm.145026
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