【摘要】 主要研究了一些对应于万有Teichmuller空间Pre-Schwarz导数模型中点的函数的拟共形扩张,得到了函数的拟共形扩张的复伸张与之Pre-Schwarz导数范数的一些关系,最后,通过具体构造一类函数的拟共形扩张表达式,得到了角域的Pre-Schwarz导数单叶性内径下界估计的另一种证明方法。更多还原

【Abstract】 This paper investigates some quasiconformal extensions of the functions cor- responding to the points in the universal Teichmuller space by Pre-Schwarzian derivative, and finds some connections between the complex dilatations of the quasiconformal extension functions and the norms of the Pre-Schwarzian derivatives.In the last section of the paper, the authors find another proof for the lower bound of the inner radius of univalency for an- gular domains by constructing an explicit quasieonformal extension of a class of holomorphic functions.更多还原