Ahlfors theory

Ahlfors theory is a mathematical theory invented by Lars Ahlfors as a geometric counterpart of the Nevanlinna theory. Ahlfors was awarded one of the two very first Fields Medals for this theory in 1936.

It can be considered as a generalization of the basic properties of covering maps to the maps which are "almost coverings" in some well defined sense. It applies to bordered Riemann surfaces equipped with conformal Riemannian metrics.