A geometric property of quadrilaterals

Authors

  • Efstathios-Konstantinos Chrontsios-Garitsis University of Illinois Urbana-Champaign, Department of Mathematics, and University of Tennessee, Knoxville, Department of Mathematics
  • Aimo Hinkkanen University of Illinois Urbana-Champaign, Department of Mathematics
DOI: https://doi.org/10.54330/afm.145026

Keywords:

Jordan domains, quadrilaterals, interior distances, quasiconformal mappings

Abstract

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 \(K\).

 

Issue
Vol. 49 No. 1 (2024)
Section
Articles

Published

2024-04-16

How to Cite

Chrontsios-Garitsis, E.-K., & Hinkkanen, A. (2024). A geometric property of quadrilaterals. Annales Fennici Mathematici, 49(1), 281–302. https://doi.org/10.54330/afm.145026

Copyright (c) 2024 Annales Fennici Mathematici

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