【作者】 李雪梅；

【导师】 程涛；

【作者基本信息】 华东师范大学 ， 基础数学， 2024， 硕士

【摘要】 本文主要研究单位圆上局部单叶解析函数的有限叶问题.已知在单位圆上,当局部单叶解析函数f与解析函数Hθ=z/(1-ze-iθ),θ∈[0,2π)之差的pre-Schwarz导数的范数小于1时,f在单位圆上整体是单叶的.本文以其差对应的pre-Schwarz导数的范数的上极限为出发点,给出一定的条件,证明了若该上极限小于1,那么f是有限叶的.更多还原

【Abstract】 This paper mainly studies the bounded valence problem of locally univalent analytic function in the unit disk.As we all know that,in the unit disk,if the norm of the pre-Schwarzian derivative of the difference between the locally univalent analytic function f and the analytic function Hθ=z/(1-ze-iθ),θ∈[0,2π)is less than 1,f is globally univalent in the unit disk.Taking the upper limit of the norm of the pre-Schwarzian derivative as the starting point,this paper gives some conditions and proves that if the upper limit is less than 1,then f is bounded valence.更多还原