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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 themaps which are "almost coverings" in some well defined sense. It applies to bordered Riemann surfaces equipped with conformal Riemannian metrics.
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