Extension and Distortion of Quasiconformal Mapping

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

Chapter Chapter 3 in Quasiconformal Mappings in the Plane and Complex Dynamics, 2025, pp 55-92 from Springer

Abstract: Abstract Extension of quasiconformal mapping (to measure 0 set, to region boundary by Beurling-Ahlfors extension with quasisymmetric functions, to free arc of region boundary with upper bounds of the dilatation, by reflection). Quasiconformal curves, quasiconformal reflections, curves with bounded bending, characterizations of quasiconformal Jordan curves. Sewing at a Jordan curve. Distortion properties of quasiconformal mappings, including the Mori theorem. Equicontinuity, Hölder continuity and normality equivalence for families of quasiconformal mappings. Nucleous of sequence of sets of complex numbers and related property of quasiconformal mappings. Circular dilatation. Quasiconformality of monotome functions. Application of the measurable Riemann mapping and the Mori theorems to obtain the Leau-Fatou conjugacy of complex dynamics in a neighborhood of a parabolic fixed point.

Date: 2025
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DOI: 10.1007/978-3-031-80115-0_3

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