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arXiv · 2303.17337

A geometric property of quadrilaterals

Efstathios Konstantinos Chrontsios Garitsis·Aimo Hinkkanen
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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 $K$.

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Efstathios Konstantinos Chrontsios Garitsis, Aimo Hinkkanen. 2023-03-30. A geometric property of quadrilaterals. https://arxiv.org/abs/2303.17337

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