Value Distribution Theory and Related Topics

1. Front Matter

   Pages i-vii

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2. Geometric value distribution theory

   1. A New Program of Investigations in Analysis: Gamma-Lines Approaches

      • G. Barsegian

      Pages 1-73

   2. On Level Sets of Quasiconformal Mappings

      • G. A. Sukiasyan

      Pages 75-92

3. Classical value distribution theory

   1. On the Unintegrated Nevanlinna Fundamental Inequality for Meromorphic Functions of Slow Growth

      • Angel Alonso, Arturo Fernández, Javier Pérez

      Pages 93-104

   2. On Some New Concept of Exceptional Values

      • G. A. Barsegian, C. C. Yang

      Pages 105-116

   3. Maximum Modulus Points, Deviations and Spreads of Meromorphic Functions

      • E. Ciechanowicz, I. I. Marchenko

      Pages 117-129

   4. Composition Theorems, Multiplier Sequences and Complex Zero Decreasing Sequences

      • Thomas Craven, George Csordas

      Pages 131-166

   5. Nevanlinna Theory in an Annulus

      • Risto Korhonen

      Pages 167-179

   6. On Strong Asymptotic Tracts of Functions Holomorphic in a Disk

      • I. I. Marchenko, I. G. Nikolenko

      Pages 181-188

4. Complex differential and functional equations

   1. A New Trend in Complex Differential Equations: Quasimeromorphic Solutions

      • G. A. Barsegian, A. A. Sarkisian, C. C. Yang

      Pages 189-199

   2. On the Functional Equation P(F)=Q(G)

      • Ha Huy Khoai, Yang C. C.

      Pages 201-207

   3. Value Distribution of the Higher Order Analogues of the First Painlevé Equation

      • Yuzan He

      Pages 209-217

   4. Some Further Results on the Functional Equation P(F)=Q(G)

      • Chung-Chun Yang, Ping Li

      Pages 219-231

5. Several variables theory

   1. Recent Topics in Uniqueness Problem for Meromorphic Mappings

      • Yoshihiro Aihara

      Pages 233-263

   2. On Interpolation Problems in Cn

      • Carlos A. Berenstein, Bao Qin Li

      Pages 265-279

   3. Jet Bundles and its Applications in Value Distribution of Holomorphic Mappings

      • Pei-Chu Hu, Chung-Chun Yang

      Pages 281-319

   4. Normal Families of Meromorphic Mappings of Several Complex Variables into the Complex Projective Space

      • Zhen-Han Tu

      Pages 321-333

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.

• Complex analysis
• Meromorphic function
• Nevanlinna theory
• calculus
• differential equation
• functional equation
• maximum
• ordinary differential equations

• National Academy of Sciences of Armenia, Yerevan, Armenia

  G. Barsegian

• University of Joensuu, Joensuu, Finland

  I. Laine

• Hong Kong University of Science and Technology, Hong Kong, China

  C. C. Yang

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