Branch values in Ahlfors' theory of covering surfaces
Complex Variables
2018-10-17 v1
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)
Keywords
Cite
@article{arxiv.1810.06857,
title = {Branch values in Ahlfors' theory of covering surfaces},
author = {Zonghan Sun and Guangyuan Zhang},
journal= {arXiv preprint arXiv:1810.06857},
year = {2018}
}
Comments
This paper is a preparation for the further research on Ahlfors' theorey of covering surfaces