拟对称映射的最大伸缩商与边界伸缩商  

The Maximal Dilatation and Boundary Dilatation of Quasi-symmetric Mapping

作　　者：漆毅[1,2] 吴艳[3] 

机构地区：[1]北京航空航天大学数学系 [2]数学,信息与行为教育部重点实验室,北京100083 [3]临沂师范学院数学系,山东276005

出　　处：《数学物理学报（A辑）》2007年第5期839-844,共6页Acta Mathematica Scientia

基　　金：国家自然科学基金(10571009)资助

摘　　要：文献[1]在研究单位圆周■△上的拟对称自同胚的最大伸缩商与极值最大伸缩商之间的关系时,证明了:如果拟对称自同胚h的最大伸缩商Kq(h)不能在某个以开单位圆盘△为域、顶点在单位圆周■△上的拓扑四边形Q处达到,则一定有Kq(h)≤H(h)成立,其中H(h)为h的边界伸缩商.这一结论在文献[1]中起着重要作用,但证明比较烦琐.该文主要给出该结论一个简单的证明,并且利用这一结论研究拟对称自同胚的最大伸缩商何时可以在某个拓扑四边形上达到.　To study the relationship between the maximal dilatation of quasi-symmetric self-homoemorphism of the unit circle and the maximal dilatation of its extremal extension, it was proved in [1] that if the maximal dilatation Kq（h） of a qusi-symmetric self-homoemorphism h cannot be arrive at some quadrilateral with the unit disk A as its domain and vertices on the unit circle δ△, then Kq（h）≤H（h）, where H（h） is the boundary dilatation of h. The main resluts in [1] quite depend on this result. But its proof there is very complicated. In this paper, the authors give another elementary and simple proof. Furthermore, they use this result to study the problem when the maximal dilatation of a qusi-symmetric self-homoemorphism of the unit circle could be arrive at some quadrilateral.

关 键 词：拟共形映射 拟对称白同胚 TEICHMULLER空间 

分 类 号：O174.55[理学—数学]