共查询到19条相似文献,搜索用时 62 毫秒
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拟共形映射能较好地保持角度,在形状编辑等几何处理领域有着广泛应用.但该类映射不易构造,特别是复杂区域之间的拟共形映射构造,是一个困难且重要的问题.本文研究了一类简单的拟共形映射,即双线性映射,讨论了其伸缩率的分布情况,证明了伸缩率的最大值一定在四边形区域的顶点上取得.相关结论为复杂区域之间拟共形映射的构造提供了良好的理论基础.数值实验验证了结论的正确性. 相似文献
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具有边界对应的拟共形扩张的伸缩商估计 总被引:1,自引:0,他引:1
本文研究了拟共形映射的极值问题.利用Beurling-Ahlfors扩张函数,获得了一类新的拟共形映射,推广了文献[1]的结果. 相似文献
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证明了(1)■中真子域D上的Apollonian度量αD是拟共形映射的拟不变量;(2)■中严格一致域是拟共形不变的;(3)■中的Jordan域D是拟圆当且仅当D是严格一致域,作为应用,进一步得到了Apollonian边界条件,拟共形映射和局部Lipschitz映射之间的关系。 相似文献
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在研究拟共形映射的唯一极值性时,Reich引入了具有不可缩伸缩商的拟共形映射的概念.本文将继续讨论这类映射,并给出无穷小情形下的一些类似结果 相似文献
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在研究拟共形映射的唯一极值性时,Reich引入了具有不可缩伸缩商的拟共形映射的概念.本文将继续讨论这类映射,并给出无穷小情形下的一些类似结果. 相似文献
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证明了(1)(-R)n中真子域D上的Apollonian度量aD是拟共形映射的拟不变量;(2)(-R)n中严格一致域是拟共形不变的;(3)(-R)2中的Jordan域D是拟圆当且仅当D是严格一致域.作为应用,进一步得到了Apollonian边界条件,拟共形映射和局部Lipschitz映射之间的关系. 相似文献
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韩丹丹 《数学的实践与认识》2018,(12)
考察了中的闭集的Hausdorff维数在渐近共形映射下的不变性,以及拟圆周的Hausdorff维数和拟共形映射的边界伸缩商的关系,证明了中的闭集的Hausdorff维数在渐近共形映射下是不变的,给出了拟圆周的Hausdorff维数与边界伸缩商的一个不等式的简单证明,在某种意义上推广了相关的两个结果. 相似文献
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In their paper [17], Sullivan and Thurston introduced the notion of quasiconformal motions, and proved an extension theorem for quasiconformal motions over an interval. We prove some new properties of (normalized) quasiconformal motions of a closed set E in the Riemann sphere, over connected Hausdorff spaces. As a spin-off, we strengthen the result of Sullivan and Thurston, and show that if a quasiconformal motion of E over an interval has a certain group-equivariance property, then the extended quasiconformal motion can be chosen to have the same group-equivariance property. Our main theorem proves a result on isomorphisms of continuous families of Möbius groups arising from a group-equivariant quasiconformal motion of E over a path-connected Hausdorff space. Our techniques connect the Teichmüller space of the closed set E with quasiconformal motions of E. 相似文献
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Xiaosheng Li 《Transactions of the American Mathematical Society》2005,357(6):2119-2132
In this paper we study Schottky quasiconformal groups. We show that the limit sets of Schottky quasiconformal groups are uniformly perfect, and that the limit set of a given discrete non-elementary quasiconformal group has positive Hausdorff dimension.
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The distortion property of hyperbolic area of planar quasiconformal mappings is studied in this paper.In the case of radial quasiconformal mappings and angular deformed quasiconformal mappings their hyperbolic area distortions are estimated quite sharply.The result can be applied to judge whether the hyperbolic area of a planar subset is explodable. 相似文献
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We characterize quasiconformal mappings as those homeomorphisms between two metric measure spaces of locally bounded geometry
that preserve a class of quasiminimizers. We also consider quasiconformal mappings and densities in metric spaces and give
a characterization of quasiconformal mappings in terms of the uniform density property introduced by Gehring and Kelly. 相似文献
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Zoltán M. Balogh 《Journal d'Analyse Mathématique》2001,83(1):289-312
We construct quasiconformal mappings on the Heisenberg group which change the Hausdorff dimension of Cantor-type sets in an
arbitrary fashion. On the other hand, we give examples of subsets of the Heisenberg group whose Hausdorff dimension cannot
be lowered by any quasiconformal mapping. For a general set of a certain Hausdorff dimension we obtain estimates of the Hausdorff
dimension of the image set in terms of the magnitude of the quasiconformal distortion. 相似文献
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《复变函数与椭圆型方程》2012,57(15):1107-1115
In this article, we discuss the minimal mappings of Douglas–Dirichlet functional and harmonic quasiconformal mappings, and solve the uniqueness problem of harmonic quasiconformal mappings posed by Shibata. 相似文献
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Modular equations occur in number theory, but it is less known that such equations also occur in the study of deformation
properties of quasiconformal mappings. The authors study two important plane quasiconformal distortion functions, obtaining
monotonicity and convexity properties, and finding sharp bounds for them. Applications are provided that relate to the quasiconformal
Schwarz Lemma and to Schottky’s Theorem. These results also yield new bounds for singular values of complete elliptic integrals.
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Fei Yang 《数学学报(英文版)》2013,29(11):2047-2072
We prove that for any bounded type irrational number 0θ1,the boundary of the Siegel disk of fα(z)=e2πiθsin(z)+αsin3(z),α∈C,which centered at the origin,is a quasicircle passing through 2,4 or 6 critical points of fαcounted with multiplicity. 相似文献
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本文讨论了Nehari函数族的偏差性质,得到了这类函数及其导数的若干偏差定理,同时研究了这类函数的拟共形延拓,并给出拟共形延拓的精确表达式. 相似文献