请输入您要查询的字词:

 

单词 Koebe14Theorem
释义

Koebe 1/4 theorem


Theorem (Koebe).

Suppose f is a schlicht functionMathworldPlanetmath (univalent functionMathworldPlanetmath on the unit discsuch that f(0)=0 and f(0)=1) and DC is the unit disc in the complex planeMathworldPlanetmath, then

f(𝔻){w|w|<1/4}.

That is, if a univalent function on the unit disc maps 0 to 0 and has derivative1 at 0, then the image of the unit disc contains the ball of radius 1/4. So for any wf(𝔻) we have that |w|1/4. Furthermore, if we look at the Koebe function, we can see that the constant 1/4 is sharp and cannot be improved.

References

  • 1 John B. Conway..Springer-Verlag, New York, New York, 1995.
随便看

 

数学辞典收录了18232条数学词条,基本涵盖了常用数学知识及数学英语单词词组的翻译及用法,是数学学习的有利工具。

 

Copyright © 2000-2023 Newdu.com.com All Rights Reserved
更新时间:2025/5/4 18:55:23