A counterexample theorem in quasiconformal mapping theory  

作　　者：沈玉良 

机构地区：[1]Department of Mathematics, Suzhou University, Suzhou 215006, China

出　　处：《Science China Mathematics》2000年第9期929-936,共8页中国科学：数学（英文版）

摘　　要：Given a quasisymmetric homeomorphismh of the unit circle onto itself, denote byK n * ,H h andK h the extremal maximal dilatation, boundary dilatation and maximal dilatation ofh, respectively. It is proved that there exists a family of quasisymmetric homeomorphismsh such thatK h <H h =K h * This gives a negative answer to a problem asked independently by Wu and Yang. Furthermore, some related topics are also discussed.Given a quasisymmetric homeomorphism h of the unit circle onto itself, denote by Kh* , Hh and Kh the extremal maximal dilatation, boundary dilatation and maximal dilatation of h, respectively. It is proved that there exists a family of quasisymmetric homeomoiphisms h such that Kh &lt; Hh = Kh* . This gives a negative answer to a problem asked independently by Wu and Yang. Furthermore, some related topics are also discussed.

关 键 词：quasisymmetric HOMEOMORPHISM EXTREMAL MAXIMAL DILATATION boundary DILATATION MAXIMAL di-latation . 

分 类 号：O157.5[理学—数学]