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Distribution of Values of Holomorphic Mappings
 
Front Cover for Distribution of Values of Holomorphic Mappings
Available Formats:
Electronic ISBN: 978-1-4704-4475-4
Product Code: MMONO/61.E
List Price: $101.00
MAA Member Price: $90.90
AMS Member Price: $80.80
Front Cover for Distribution of Values of Holomorphic Mappings
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Distribution of Values of Holomorphic Mappings
Available Formats:
Electronic ISBN:  978-1-4704-4475-4
Product Code:  MMONO/61.E
List Price: $101.00
MAA Member Price: $90.90
AMS Member Price: $80.80
  • Book Details
     
     
    Translations of Mathematical Monographs
    Volume: 611985; 225 pp
    MSC: Primary 32;

    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.

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • The Characteristic and Counting Functions
    • The Main Theorems of Value Distribution Theory
    • Holomorphic Curves
    • Generalization of the Main Theorems
    • Further Results
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Volume: 611985; 225 pp
MSC: Primary 32;

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.

  • Chapters
  • Introduction
  • The Characteristic and Counting Functions
  • The Main Theorems of Value Distribution Theory
  • Holomorphic Curves
  • Generalization of the Main Theorems
  • Further Results
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