Definitions of Quasiconformal Mapping in the Plane

Luis T. Magalhães
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Luis T. Magalhães: University of Lisbon, Instituto Superior Técnico

Chapter Chapter 1 in Quasiconformal Mappings in the Plane and Complex Dynamics, 2025, pp 1-39 from Springer

Abstract: Abstract Regular quasiconformal mappings in the plane. Geometric definition of quasiconformal mapping. Extremal length, quadrilateral and ring module and their basic properties. Extremals of ring modules (Teichmüller, Mori. Grötsch). Analytic definition of quasiconformal mapping, with Beltrami equation including the Weyl lemma and the notion of absolutely continuous functions on lines as function from subsets of ℝ 2 $$\mathbb {R}^2$$ to ℝ 2 $$\mathbb {R}^2$$ .

Date: 2025
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DOI: 10.1007/978-3-031-80115-0_1

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