Value Distribution Theory and Related Topics

G. Barsegian (auth.), G. Barsegian, I. Laine, C. C. Yang (eds.)1402079516, 1402079508

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.

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Table of contents :
A New Program of Investigations in Analysis: Gamma-Lines Approaches….Pages 1-73
On Level Sets of Quasiconformal Mappings….Pages 75-92
On the Unintegrated Nevanlinna Fundamental Inequality for Meromorphic Functions of Slow Growth….Pages 93-104
On Some New Concept of Exceptional Values….Pages 105-116
Maximum Modulus Points, Deviations and Spreads of Meromorphic Functions….Pages 117-129
Composition Theorems, Multiplier Sequences and Complex Zero Decreasing Sequences….Pages 131-166
Nevanlinna Theory in an Annulus….Pages 167-179
On Strong Asymptotic Tracts of Functions Holomorphic in a Disk….Pages 181-188
A New Trend in Complex Differential Equations: Quasimeromorphic Solutions….Pages 189-199
On the Functional Equation P(F)=Q(G) ….Pages 201-207
Value Distribution of the Higher Order Analogues of the First Painlevé Equation….Pages 209-217
Some Further Results on the Functional Equation P(F)=Q(G) ….Pages 219-231
Recent Topics in Uniqueness Problem for Meromorphic Mappings….Pages 233-263
On Interpolation Problems in C n ….Pages 265-279
Jet Bundles and its Applications in Value Distribution of Holomorphic Mappings….Pages 281-319
Normal Families of Meromorphic Mappings of Several Complex Variables into the Complex Projective Space….Pages 321-333