Acta Scientiarum Naturalium Universitatis Pekinensis

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Capacity and Covering Theorems

FANG Qiqing, ZHANG Shunyan   

  1. Department of Mathematics, Peking University, Beijing, 100871
  • Received:1993-08-04 Online:1995-01-20 Published:1995-01-20



  1. 北京大学数学系,北京,100871

Abstract: Suppose that G and G~ are domains in C- with ∞ included. Assume that f: GG~is meromorphic with a pole of order m at ∞. Let E=C~\G and F=C~\G~ be compact sets. Under some conditions on f(see Theorem 1), two inequalities concerning cap E and cap F are given. By using these inequalities several covering theorems are obtained.

Key words: capacity, Green's function

摘要: GG~为扩充复平面C-上的区域,且含有∞点,又设f:GG~为半纯函数,∞为它的级极点,令 E=C~\GF=C~\G~,显然E,F为紧集,本文给出容量capE与capF比较的两个不等式,并利用这些不等式得到了几个有趣的掩蔽定理。

关键词: 容量, Green函数

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