Equilateral triangle skew condition for quasiconformality
Colleen Ackermann, Peter Ha\"issinsky (I2M), Aimo Hinkkanen
TL;DR
This paper characterizes quasiconformal mappings by examining how they distort the vertices of equilateral triangles, providing a geometric criterion for quasiconformality.
Contribution
It introduces a new geometric condition based on equilateral triangle distortion to identify quasiconformal mappings.
Findings
Quasiconformal mappings preserve a specific equilateral triangle distortion property.
The geometric criterion is both necessary and sufficient for quasiconformality.
This characterization simplifies the understanding of quasiconformal mappings through geometric distortion.
Abstract
We characterize quasiconformal mappings in terms of the distortion of the vertices of equilateral triangles.
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Taxonomy
TopicsAnalytic and geometric function theory · Geometric Analysis and Curvature Flows · Algebraic and Geometric Analysis