Ahlfors拟共形扩张条件与类$Φ$
Ahlfors's quasiconformal extension condition and $Φ$-likeness
摘要：
$Φ$ -like函数的概念被认为是单叶性的充要条件。应用这一思想，我们得到了单位圆盘上的解析函数不仅是单叶函数而且是黎曼球面的拟共形扩张的几个必要条件和充分条件，作为著名的单叶函数和拟共形扩张准则，特别是Ahlfors的拟共形扩张条件的推广.
英文摘要：
The notion of $Φ$-like functions is known to be a necessary and sufficient condition for univalence. By applying the idea, we derive several necessary conditions and sufficient conditions for that an analytic function defined on the unit disk is not only univalent but also has a quasiconformal extension to the Riemann sphere, as generalizations of well-known univalence and quasiconformal extension criteria, in particular, Ahlfors's quasiconformal extension condition.
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