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Branch values in Ahlfors’ theory of covering surfaces

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Abstract

In the study of the constant in Ahlfors’ second fundamental theorem involving a set Eq consisting of q points, branch values of covering surfaces outside Eq bring a lot of troubles. To avoid this situation, for a given surface Σ0, it is useful to construct a new surface Σ1, such that L(∂Σ1) ⩽ L(∂Σ0), and H(Σ1, Eq) ⩾ H (Σ0, Eq), and all branch values of Σ1 are contained in Eq. The goal of this paper is to prove the existence of such Σ1, which generalizes a result found by Zhang (2013).

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 11531007).

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Authors and Affiliations

  1. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China

    Zonghan Sun & Guangyuan Zhang

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  1. Zonghan Sun
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  2. Guangyuan Zhang
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Correspondence to Guangyuan Zhang.

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Sun, Z., Zhang, G. Branch values in Ahlfors’ theory of covering surfaces. Sci. China Math. 63, 1535–1558 (2020). https://doi.org/10.1007/s11425-018-9514-3

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  • DOI: https://doi.org/10.1007/s11425-018-9514-3

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