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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 \(\mathbb {R}^2\) to \(\mathbb {R}^2\) .

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Definitions of Quasiconformal Mapping in the Plane

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  • 发表日期：

    2025年

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  • Luis T. Magalhães

摘要

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 \(\mathbb {R}^2\) to \(\mathbb {R}^2\) .