Abstract
By the classical definition, a quasiconformal mapping is a sense-preserving diffeomorphism of a plane domain onto another plane domain which maps infinitesimal circles onto infinitesimal ellipses with a uniformly bounded ratio of axes. Later it was found preferable to relax a priori differentiability conditions and define a quasiconformal mapping in the plane as a sense-preserving homeomorphism which leaves some conformai invariant quasi — invariant. The most general conformai invariant suitable for this purpose is the module of a path family. The precise requirement for quasiconfrormality is the existence of a fixed constant K such that the module of every path family lying in the domain in which the homeomorphism is considered increases at most K times.
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© 1984 Birkhäuser Verlag Basel
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Lehto, O. (1984). A Historical Survey of Quasiconformal Mappings. In: Knobloch, E., Louhivaara, I.S., Winkler, J. (eds) Zum Werk Leonhard Eulers. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7121-1_12
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DOI: https://doi.org/10.1007/978-3-0348-7121-1_12
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