[1]赖万才.拟共形映照的一个极值问题[J].华侨大学学报(自然科学版),1989,10(4):359-363.[doi:10.11830/ISSN.1000-5013.1989.04.0359]
　Lai Wancai.An Extremal Problem for Quasiconformal Mappings[J].Journal of Huaqiao University(Natural Science),1989,10(4):359-363.[doi:10.11830/ISSN.1000-5013.1989.04.0359]
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拟共形映照的一个极值问题()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第10卷
期数:
1989年第4期
页码:
359-363
栏目:
出版日期:
1989-10-20

文章信息/Info

Title:
An Extremal Problem for Quasiconformal Mappings
作者:
赖万才
华侨大学应用数学系
Author(s):
Lai Wancai
关键词:
拟共形映照;  极值问题;  非欧尺度
Keywords:
quasi-conformal mappings;  extremal problem;  non-Euclidean metric
DOI:
10.11830/ISSN.1000-5013.1989.04.0359
摘要:
本文证明:如果f(z)是拓广复平面到自身使得f(0)=0,f(1)=1和f(∞)=∞的一个Q拟共形映照。则对任何r,|z|≤r |f(z)|≤r,成立|f(z)-z|≤4/π rK(1/1+r)K(r/1+r)·logQ,其中K(t)=integral from n=0 to 1(dx/((1-x2)(1-tx2))1/2。它是夏道行的一个定理的拓广。
Abstract:
In this paper the author proves: If f(z) is a quasiconformal mapping of the extended complex plane onto itself such that f(0)=0, f(1)=1 and f(∞)=∞, then |f(z)-z|≤4π rK (1/1+r)K(r1+r)lig Q holds for any r, |z|≤r and |f(z)|≤r, where K (t)=integral from 1 to

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更新日期/Last Update: 2014-03-22