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arXiv · 1810.06857

Branch values in Ahlfors' theory of covering surfaces

Zonghan Sun·Guangyuan Zhang
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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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Zonghan Sun, Guangyuan Zhang. 2018-10-16. Branch values in Ahlfors' theory of covering surfaces. https://arxiv.org/abs/1810.06857

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