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Mbius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.
出处
《数学的实践与认识》
CSCD
北大核心
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)
