Quadrilaterals, extremal quasiconformal extensions and Hamilton sequences

作     者：CHEN Zhi-guo ZHENG Xue-liang YAO Guo-wu 

作者机构：Department of Mathematics Zhejiang University Hangzhou 310028 China Department of Mathematics Taizhou College Linhai 317000 China Department of Mathematical Sciences Tsinghua University Beijing 100084 China 

出 版 物：《Applied Mathematics(A Journal of Chinese Universities)》 (高校应用数学学报（英文版）（B辑）)

年 卷 期：2010年第25卷第2期

页      面：217-226页

核心收录：

学科分类：080904[工学-电磁场与微波技术] 07[理学] 0809[工学-电子科学与技术（可授工学、理学学位）] 08[工学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Supported by the National Natural Science Foundation of China(10671174, 10401036) a Foundation for the Author of National Excellent Doctoral Dissertation of China(200518) 

主　　题：Extremal quasiconformal mapping quasisymmetric mapping Hamilton sequence substantial boundary point. 

摘      要：The relationship between Strebel boundary dilatation of a quasisymmetric function h of the unit circle and the dilatation indicated by the change in the modules of the quadrilaterals with vertices on the circle intrigues many mathematicians. It had been a conjecture for some time that the dilatations Ko（h） and K1（h） of h are equal before Anderson and Hinkkanen disproved this by constructing concrete counterexamples. The independent work of Wu and of Yang completely characterizes the condition for Ko（h） = K1 （h） when h has no substantial boundary point. In this paper, we give a necessary and sufficient condition to determine the equality for h admitting a substantial boundary point.