共查询到20条相似文献,搜索用时 15 毫秒
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Work done with support from NSF grant MCS 83-00248. 相似文献
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C. Wayne Mastin Joe F. Thompson 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1978,29(1):1-11
Summary Some basic properties of quasiconformal mappings are reviewed which leads to the development of discrete analogs of quasiconformal mappings of a multiply connected domain onto a rectangular domain with slits. These discrete mappings can be constructed by solving a system of equations. Comparison of results for a special conformal mapping suggest that the discrete mapping is a good approximation to the quasiconformal mapping.
Zusammenfassung Es werden einige grundlegende Eigenschaften quasikonformer Abbildungen diskutiert, und es wird ein diskretes Analogon solcher Abbildungen aufgestellt, mit Hilfe dessen mehrfach zusammenhängende Bereiche auf Rechteckbereiche mit Schlitzen abgebildet werden können. Ein Vergleich der Resultate für eine spezielle konforme Abbildung zeigt, dass die diskrete Abbildung eine gute Approximation der quasikonformen Abbildung liefert.相似文献
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Extremal quasiconformal mappings 总被引:4,自引:0,他引:4
S. L. Krushkal' 《Siberian Mathematical Journal》1969,10(3):411-418
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Aimo Hinkkanen 《Mathematische Zeitschrift》1983,183(4):539-545
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We show that quasiconformal mappings on strongly pseudoconvex hypersurfaces satisfy a system of Beltrami equations. In particular, the 1-quasiconformal mappings on these surfaces are CR or anti-CR mappings. Furthermore, if these surfaces are also real-analytic and nonspherical, then 1-quasiconformal mappings on them, which fix a point, can be linearized. 相似文献
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Konstantin M Dyakonov 《Advances in Mathematics》2004,187(1):146-172
We discuss the implication , where f is a holomorphic function (resp., a quasiconformal mapping) on a domain (resp., ) and Λω(G) is the Lipschitz space associated with a majorant ω. 相似文献
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HUANG HuaYing & WU ShengJian LMAM School of Mathematical Sciences Peking University Beijing China 《中国科学 数学(英文版)》2010,(5)
We show that the extremal polygonal quasiconformal mappings are biLipschitz with respect to the hyperbolic metric in the unit disk. 相似文献
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A. G. Sergeev 《Mathematical Notes》2016,100(1-2):123-131
The quantum interpretation of quasisymmetric homeomorphisms of the circle, i.e., homeomorphisms that can be extended to quasiconformal homeomorphisms of the unit disk, and their relationship to basic constructions of quantum calculus are discussed. 相似文献
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Ze Min Zhou 《数学学报(英文版)》2013,29(8):1543-1554
A homeomorphism w=f(z) of a domain D is called a locally quasiconformal mapping, if for each subdomain D' of D with 'D, the restriction of f(z) on D' is a quasiconformal mapping. We give some conditions for a measurable function μ(z) on the unit disc to be the complex dilatation of a locally quasiconformal mapping f which can be homeomorphically extended to the closed unit disc. 相似文献
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V. I. Ryazanov 《Siberian Mathematical Journal》1996,37(2):325-334
The research was partly supported by the International Science Foundation (Grant U 96 000). 相似文献
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Shen Yu-Liang 《Proceedings of the American Mathematical Society》2000,128(1):135-139
Given a family of quasiconformal deformations such that has a uniform bound , the solution of the Löwner-type differential equation
is an -quasiconformal mapping. An open question is to determine, for each fixed , whether the extremality of is equivalent to that of . The note gives this a negative approach in both directions.
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Yu. E. Alenitsyn 《Siberian Mathematical Journal》1979,20(3):447-449
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K. Strebel 《Commentarii Mathematici Helvetici》1999,74(1):143-149
A polygon P
N is the unit disk with distinguished boundary points, . An extremal quasiconformal mapping maps each polygon inscribed in onto a polygon inscribed in . Let f
N be the extremal quasiconformal mapping of P
N onto P'
N. Let K
N be its dilatation and let K
0 be the maximal dilatation of f
0. Then, evidently . The problem is, when equality holds. This is completely answered, if f
0 does not have any essential boundary points. For quadrilaterals Q and Q' = f
0
(Q) the problem is sup(M'/M) = K
0, with M and M' the moduli of Q and Q' respectively.
Received: December 23, 1997 相似文献
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In any Carnot (nilpotent stratified Lie) group G of homogeneous dimension Q, Green's function u for the Q-Laplace equation exists and is unique. We prove that there exists a constant so that is a homogeneous norm in G. Then the extremal lengths of spherical ring domains (measured with respect to N) can be computed and used to give estimates for the extremal lengths of ring domains measured with respect to the Carnot-Carathéodory
metric. Applications include regularity properties of quasiconformal mappings and a geometric characterization of bi-Lipschitz
mappings.
Received: 18 September 2000/ revised version: 19 November 2001 / Published online: 17 June 2002 相似文献
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