Branch values in Ahlfors' theory of covering surfaces

2018/10/16 by Zonghan Sun, Sun, Zonghan, Guangyuan Zhang +1
Computer Science · Engineering · #30D35 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Analysis Techniques #Complex Variables (math.CV) #Computational Geometry and Mesh Generation #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1810.06857

openalex publication_date 2018/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the study of the constant in Ahlfors' second fundamental theorem involving a set E_q of q points, branch values of covering surfaces outside E_q bring a lot of troubles. To avoid this situation, for a given surface S, it is useful to construct a new surface So such that L(So) <=L(S), and H(S)>=H(S), and all branch values of So are contained in E_q. The goal of this paper is to prove the existence of such So, which generalizes Lemma 9.1 and Theorem 10.1 in Zhang G.Y.: The precise bound for the area-length ratio in Ahifors' theory of covering surfaces. Invent math 191:197-253(2013)

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