In the mathematical field of complex analysis, Nevanlinna theory is part of the theory of meromorphic functions. It was introduced by Nevanlinna (1925). In the opinion of Hermann Weyl, appearance of Nevanlinna's paper "has been one of the few great mathematical events of our century". The question addressed by the theory is to describe when a meromorphic function on the complex plane, or more generally some complex manifold, to some other manifold is necessarily constant. A fundamental tool is to find ways of measuring the rate of growth of such a function.
Other main contributors in the first half of the 20th century were Lars Ahlfors, André Bloch, Henri Cartan, Edward Collingwood, Otto Frostman, Frithiof Nevanlinna, Henrik Selberg, Tatsujiro Shimizu, Oswald Teichmüller, and Georges Valiron. In its original form, Nevanlinna theory deals with meromorphic functions of one complex variable defined in a disc |z| < R or in the whole complex plane (R = ∞). Subsequent generalizations extended Nevanlinna theory to algebroid functions, holomorphic curves, holomorphic maps between complex manifolds of arbitrary dimension, quasiregular maps and minimal surfaces.
This article describes mainly the classical version for meromorphic functions of one variable, with emphasis on functions meromorphic in the complex plane. General references for this theory are Goldberg & Ostrovskii, Hayman and Lang (1987).
Read more about Nevanlinna Theory: First Fundamental Theorem, Second Fundamental Theorem, Defect Relation, Applications, Further Development
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