Vector valued Nevanlinna theory

Cover......Page 1
Title Page......Page 2
Copyright Page......Page 3
Dedication......Page 4
Contents......Page 6
Preface......Page 8
1 Generalization of the Formula of Poisson-Jensen-Nevanlinna......Page 14
2 Interpretation by Hermitian Geometry......Page 22
3 The Generalized First Main Theorem......Page 29
4 The Example of Rational Vector Functions......Page 40
5 Properties of V(r,a)......Page 47
6 Properties of T(r,f)......Page 52
7 The Connection of T(r,f),m(r,f) and N(r,f) with T(r,f ] .),m(r,f ] .) and N(r,f J .)......Page 58
8 The Order of Growth......Page 64
9 The Generalized Ahlfors-Shimizu Characteristic T(r,f)......Page 71
10 The Generalized Riemann Sphere......Page 81
11 The Spherical Normal Form of the Generalized First Main Theorem......Page 86
12 The Mean Value Representation of T(r,f)......Page 88
13 The Genus of a Meromorphic Vector Function......Page 95
14 Some Relations between M,m ; N,n ; V,v and A......Page 102
15 The Generalized Second Main Theorem......Page 123
16 The Generalized Deficiency Relation......Page 142
17 Further Results about Deficiencies......Page 154
Appendix: Rudiments of Complex Manifolds and Hermitian Geometry......Page 181
Bibliography......Page 202
Table of Symbols......Page 210