| dbo:abstract |
In der Funktionentheorie ist eine quasikonforme Abbildung eine Verallgemeinerung einer biholomorphen Abbildung. Hier wird im Wesentlichen auf die Winkeltreue verzichtet. (de) En mathématiques, une application quasi conforme est une fonction de deux variables réelles, dont les dérivées partielles satisfont une certaine inégalité qui étend la notion d'application conforme. De telles applications jouent un rôle central dans la théorie de Teichmüller et en dynamique holomorphe, notamment dans la démonstration du (en) par Dennis Sullivan. Par suite, elles furent utilisées avec profit notamment par Adrien Douady, John H. Hubbard et (en). (fr) In mathematical complex analysis, a quasiconformal mapping, introduced by and named by , is a homeomorphism between plane domains which to first order takes small circles to small ellipses of bounded eccentricity. Intuitively, let f : 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. (en) 擬共形映射又稱擬保角映射，原本是複分析中的一套技術手段，現已發展為一套獨立學科。其定義如下。 固定實數 。 設 為平面上的開子集，連續可微函數 保持定向。若在每一點上其導數 將圓映至離心率小於等於 之橢圓，則稱 為 -擬共形映射。由此可見共形映射是 -擬共形映射。 若存在 使 為擬共形映射，則稱 為擬共形映射。 擬共形映射的定義也可以延伸至較高維度或非連續可微的情形。 (zh) |
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https://books.google.com/books%3Fid=-M_fVxXneBkC https://books.google.com/books%3Fid=4oWFH7FPb50C https://www.ams.org/notices/200611/whatis-heinonen.pdf |
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V. A. (en) |
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Q/q076430 (en) |
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Zorich (en) |
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Quasi-conformal mapping (en) |
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In der Funktionentheorie ist eine quasikonforme Abbildung eine Verallgemeinerung einer biholomorphen Abbildung. Hier wird im Wesentlichen auf die Winkeltreue verzichtet. (de) En mathématiques, une application quasi conforme est une fonction de deux variables réelles, dont les dérivées partielles satisfont une certaine inégalité qui étend la notion d'application conforme. De telles applications jouent un rôle central dans la théorie de Teichmüller et en dynamique holomorphe, notamment dans la démonstration du (en) par Dennis Sullivan. Par suite, elles furent utilisées avec profit notamment par Adrien Douady, John H. Hubbard et (en). (fr) In mathematical complex analysis, a quasiconformal mapping, introduced by and named by , is a homeomorphism between plane domains which to first order takes small circles to small ellipses of bounded eccentricity. Intuitively, let f : 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. (en) 擬共形映射又稱擬保角映射，原本是複分析中的一套技術手段，現已發展為一套獨立學科。其定義如下。 固定實數 。 設 為平面上的開子集，連續可微函數 保持定向。若在每一點上其導數 將圓映至離心率小於等於 之橢圓，則稱 為 -擬共形映射。由此可見共形映射是 -擬共形映射。 若存在 使 為擬共形映射，則稱 為擬共形映射。 擬共形映射的定義也可以延伸至較高維度或非連續可微的情形。 (zh) |
| rdfs:label |
Quasikonforme Abbildung (de) Application quasi conforme (fr) Quasiconformal mapping (en) 拟共形映射 (zh) |
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