A geometric property of quadrilaterals

Författare

  • 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

Nyckelord:

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 \(K\).

 

Sektion
Articles

Publicerad

2024-04-16

Referera så här

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