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Unicity of Meromorphic Mappings

ISBN-10: 1402012195
ISBN-13: 9781402012198
Edition: 2003
List price: $209.00 Buy it from $62.61
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Description: This book introduces value distribution theory starting with a survey of two Nevanlinna-type main theorems and defect relations for meromorphic mappings from parabolic manifolds into projective spaces. Then the unicity theory of meromorphic  More...

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Book details

List price: $209.00
Copyright year: 2003
Publisher: Springer
Publication date: 4/30/2003
Binding: Hardcover
Pages: 467
Size: 6.25" wide x 9.25" long x 2.00" tall
Weight: 2.046
Language: English

This book introduces value distribution theory starting with a survey of two Nevanlinna-type main theorems and defect relations for meromorphic mappings from parabolic manifolds into projective spaces. Then the unicity theory of meromorphic functions or mappings is discussed systematically and the discussion also covers value distribution theory of algebroid functions of several variables and its applications in unicity theory.Audience: Graduate students and researchers involved in the fields of analysis, complex function theory of one or several variables, value distribution theory and analysis on complex manifolds.

Preface
Nevanlinna theory
Parabolic manifolds and Hermitian geometry
The first main theorem
Growths of meromorphic functions
The lemma of logarithmic derivative
Growth estimates of Wronskians
The second main theorem
Degenerate holomorphic curves
Value distribution of differential polynomials
The second main theorem for small functions
Tumura-Clunie theory
Generalizations of Nevanlinna theorem
Generalizations of Borel theorem
Uniqueness of meromorphic functions on C
Functions that share four values
Functions that share three values CM
Functions that share pairs of values
Functions that share four small functions
Functions that share five small functions
Uniqueness related to differential polynomials
Polynomials that share a set
Meromorphic functions that share the same sets
Unique range sets
Uniqueness polynomials
Uniqueness of meromorphic functions on C[superscript m]
Technical lemmas
Multiple values of meromorphic functions
Uniqueness of differential polynomials
The four-value theorem
The three-value theorem
Generalizations of Rubel-Yang's theorem
Meromorphic functions sharing one value
Unique range sets of meromorphic functions
Unique range sets ignoring multiplicities
Meromorphic functions of order [less than sign] 1
A note on the abc-conjecture
A note on Hall's conjecture
Uniqueness of meromorphic mappings
Notes on the first main theorem
The first main theorem for line bundles
The second main theorem for line bundles
Uniqueness of meromorphic mappings into P[superscript n]
Finiteness theorems
General meromorphic mappings
Dependence theorems
Propagation theorems
Uniqueness dealing with multiple values
Algebroid functions of several variables
Preliminaries
Techniques of value distribution
The second main theorem
Algebroid reduction of meromorphic mappings
The growth of branching divisors
Reduction of Nevanlinna theory
Generalizations of Malmquist theorem
Uniqueness problems
Multiple values of algebroid functions
References
Symbols
Index

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