2023/07/10 by Zhang, GUang-Yuan
#30D45 #52B60 #Complex Variables (math.CV) #FOS: Mathematics #[2020] 30D35
paper · doi:10.48550/arxiv.2307.04623
Ahlfors Second Fundamental Theorem of covering surfaces over the Riemann sphere are one of the major events in the history of function theory, which is a geometrical interpretation of the famous Nevanlinna's Second Fundamental Theorem in the theory of value distribution. The goal of this paper is to present a method to identify the precise value for that constant h in Ahlfors' SFT for covering surfaces over the unit sphere. This problem can be traced back to the early 1940s, when J. Dufresnoy first gave a numerical estimate of h for covering surfaces over a sphere. We will first prove the existence of extremal surfaces, and then we will give a formula to compute the precise value.