Quadrilaterals, extremal quasiconformal extensions and Hamilton sequences  

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

机构地区：[1]Department of Mathematics, Zhejiang University, Hangzhou 310028, China [2]Department of Mathematics, Taizhou College, Linhai 317000, China [3]Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2010年第2期217-226,共10页高校应用数学学报（英文版）（B辑）

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)

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.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.

关 键 词：Extremal quasiconformal mapping quasisymmetric mapping Hamilton sequence substantial boundary point. 

分 类 号：O171[理学—数学] TN821.8[理学—基础数学]