Quasiconformal mapping

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In mathematics, the concept of quasiconformal mapping, introduced as a technical tool in complex analysis, has blossomed into subject all its own. A conformal mapping in the plane sends small discs to other discs (to first order). A quasiconformal mapping on an open set is a continuous homeomorphism that sends small discs to small ellipses, in which the ratio of major axis to minor axis is bounded. Such mappings are in general not holomorphic functions, but play an auxiliary role in questions about such functions.