The Nevanlinna theory of value distribution of meromorphic functions,
one of the milestones of complex analysis during the last century, was
c- ated to extend the classical results concerning the distribution of
of entire functions to the more general setting of meromorphic
functions. Later on, a similar reasoning has been applied to algebroid
functions, subharmonic functions and meromorphic functions on Riemann
surfaces as well as to - alytic functions of several complex variables,
holomorphic and meromorphic mappings and to the theory of minimal
surfaces. Moreover, several appli- tions of the theory have been
exploited, including complex differential and functional equations,
complex dynamics and Diophantine equations. The main emphasis of this
collection is to direct attention to a number of recently developed
novel ideas and generalizations that relate to the - velopment of value
distribution theory and its applications. In particular, we mean a
recent theory that replaces the conventional consideration of counting
within a disc by an analysis of their geometric locations. Another such
example is presented by the generalizations of the second main theorem
to higher dimensional cases by using the jet theory. Moreover, s- ilar
ideas apparently may be applied to several related areas as well, such
as to partial differential equations and to differential geometry.
Indeed, most of these applications go back to the problem of analyzing
zeros of certain complex or real functions, meaning in fact to
investigate level sets or level surfaces.