周泽民.塌陷型极值拟共形映射的性质[J].数学年刊A辑,2011,32(4):481~488
塌陷型极值拟共形映射的性质
On Extremal Quasi-conformal Mappings of Landslide Type
  
DOI:
中文关键词:  拟共形映射  极值拟共形映射  塌陷型极值拟共形映射  
英文关键词:Quasi-conformal mappings  Extremal quasi-conformal mappings  Extremal quasi-conformal mappings of landslide type  
基金项目:国家自然科学基金(No10771153,No10971030)资助的项目
Author NameAffiliationE-mail
ZHOU Zemin Department of Mathematics,Renmin University of China,Beijing 100872,China. zzm@ruc.edu.cn 
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中文摘要:
      证明了如果$f^\mu$是单位圆$\Delta$上塌陷型极值拟共形映射, 则存在与$f^\mu$等价的极值拟共形映射$f^{\wt\mu}$以及单位圆的子区域$G$, 使得$\wt\mu(z)=0,\ \forall z \in G.$
英文摘要:
      It is shown that if $f^\mu$ is an extremal quasi-conformal mapping of landslide type, then there exists an extremal quasi-conformal mapping $f^{\wt\mu}$ with a Beltrami coefficient $\wt\mu$ and a sub-domain $G$ of the unit disk $\Delta$, such that $\wt\mu$ is Teichm\"{u}ller equivalent to $\mu$ and satisfies $\wt\mu(z)=0, \ \forall z \in G.$
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