A vast literature has grown up around the value distribution theory of
meromorphic functions, synthesized by Rolf Nevanlinna in the 1920s and
singled out by Hermann Weyl as one of the greatest mathematical
achievements of this century. The multidimensional aspect, involving
the distribution of inverse images of analytic sets under holomorphic
mappings of complex manifolds, has not been fully treated in the
literature. This volume thus provides a valuable introduction to
multivariate value distribution theory and a survey of some of its
results, rich in relations to both algebraic and differential geometry
and surely one of the most important branches of the modern geometric
theory of functions of a complex variable.
Since the book begins with preparatory material from the contemporary
geometric theory of functions, only a familiarity with the elements of
multidimensional complex analysis is necessary background to understand
the topic. After proving the two main theorems of value distribution
theory, the author goes on to investigate further the theory of
holomorphic curves and to provide generalizations and applications of
the main theorems, focusing chiefly on the work of Soviet
mathematicians.