Книга: Quasiconformal Mapping: Mathematics, Complex Analysis, Conformal Map, Homeomorphism, Ellipse, Smooth Function, Lebesgue Measure, Distribution (Mathematics), Sobolev Space, Extremal Length

High Quality Content by WIKIPEDIA articles! In mathematics, the concept of quasiconformal mapping, introduced as a technical tool in complex analysis, has blossomed into an independent subject with various applications. Informally, a conformal homeomorphism is a homeomorphism between plane domains which to first order takes small circles to small circles. A quasiconformal homeomorphism to first order takes small circles to small ellipses of bounded eccentricity. Intuitively, let ?:D ? D? be an orientation preserving homeomorphism between open sets in the plane. If f is continuously differentiable, then it is K-quasiconformal if the derivative of f at every point maps circles to ellipses with eccentricity bounded by K.