Ahlfors theory

Summary

Ahlfors theory is a geometric counterpart of Nevanlinna theory, due to Lars Ahlfors. It views a meromorphic function on a disc as a surface spread over the Riemann sphere. It compares the area of this covering surface with the length of its boundary. When the boundary is short compared with the area, the surface covers each region of the sphere about equally often. Its best-known consequence is the Ahlfors five islands theorem.