Entire functions arising from trees

作     者：Weiwei Cui Weiwei Cui

作者机构：Center for Mathematical SciencesLund UniversityLund 22100Sweden 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2021年第64卷第10期

页      面：2231-2248页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：entire function tree Shabat Riemann surface the type problem 

摘      要：Given any infinite tree in the plane satisfying certain topological conditions,we construct an entire function f with only two critical values±1 and no asymptotic values such that f-1([-1,1])is ambiently homeomorphic to the given tree.This can be viewed as a generalization of the result of Grothendieck(see Schneps(1994))to the case of infinite trees.Moreover,a similar idea leads to a new proof of the result of Nevanlinna(1932)and Elfving(1934).