Pre-Schwarz导数意义下区域之间的距离  

Distance between Domains in the Sense of Pre-Schwarz Derivative

作　　者：迟玉华[1] 漆毅[2] 

机构地区：[1]石家庄工商职业学院基础部,河北石家庄050091 [2]北京航空航天大学数学与系统科学学院,北京100191

出　　处：《数学的实践与认识》2011年第21期214-219,共6页Mathematics in Practice and Theory

基　　金：国家自然科学基金(10571009)

摘　　要：Lehto曾用Schwarz导数定义了边界多于一点的两个单连通区域的Mbius等价类之间的"距离",并猜测它是一个距离.但最近Bozin和Markovic否定了这一猜想.一个自然的问题就是:在Pre-Schwarz导数意义相应情况如何?用Pre-Schwarz导数给出了边界多于一点的两个单连通区域的仿射等价类之间的"距离",并证明了这样定义的"距离"是一个伪距离,即使将其限制在由具有解析边界的单连通区域的仿射等价类空间上也是如此.Lehto had once defined a pseudometric for two M5bius equivalences of simply connected domains with at least two boundary points and conjectured that it is a metric. But Bozin and Markovic disproved it by counterexamples. A natural problem is that what happens in the sense of Pre-Schwarz derivative？ In this paper, a pseudometric for two affine equivalences of simply connected domains with at least two boundary points is defined. It is proved that it is not a metric even restricted to the subspace of affine equivalences of simply connected domains with analytical boundary curves.

关 键 词：SCHWARZ导数 Pre—Schwarz导数 仿射变换 

分 类 号：O172.1[理学—数学]