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Nevanlinna Theory
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Artikel-Nr:
9789811067877
Veröffentl:
2017
Einband:
eBook
Seiten:
86
Autor:
Kunihiko Kodaira
Serie:
SpringerBriefs in Mathematics
eBook Typ:
PDF
eBook Format:
Reflowable eBook
Kopierschutz:
Digital Watermark [Social-DRM]
Sprache:
Englisch
Beschreibung:
This book deals with the classical theory of Nevanlinna on the value distribution of meromorphic functions of one complex variable, based on minimum prerequisites for complex manifolds. The theory was extended to several variables by S. Kobayashi, T. Ochiai, J. Carleson, and P. Griffiths in the early 1970s. K. Kodaira took up this subject in his course at The University of Tokyo in 1973 and gave an introductory account of this development in the context of his final paper, contained in this book. The first three chapters are devoted to holomorphic mappings from C to complex manifolds. In the fourth chapter, holomorphic mappings between higher dimensional manifolds are covered. The book is a valuable treatise on the Nevanlinna theory, of special interests to those who want to understand Kodaira's unique approach to basic questions on complex manifolds.
This book deals with the classical theory of Nevanlinna on the value distribution of meromorphic functions of one complex variable, based on minimum prerequisites for complex manifolds. The theory was extended to several variables by S. Kobayashi, T. Ochiai, J. Carleson, and P. Griffiths in the early 1970s. K. Kodaira took up this subject in his course at The University of Tokyo in 1973 and gave an introductory account of this development in the context of his final paper, contained in this book. The first three chapters are devoted to holomorphic mappings fromC to complex manifolds. In the fourth chapter, holomorphic mappings between higher dimensional manifolds are covered. The book is a valuable treatise on the Nevanlinna theory, of special interests to those who want to understand Kodaira's unique approach to basic questions on complex manifolds.
Preface
1. Nevanlinna Theory of One Variable (1)
1.1 metrics of compact Rimann surfaces
1.2 integral formula
1.3 holomorphic maps over compact Riemann surfaces whose genus are greater than 2
1.4 holomorphic maps over Riemann sphreres
1.5 Defect relation
2. Schwarz--Kobayashi's Lemma
2.1 Schwarz--Kobayashi's Lemma
2.2 holomorphic maps over algebraic varieties (general type)
2.3 hyperbolic measures
3. Nevanlinna Theory of One Variable (2)
3.1 holomorphic maps over Riemann shpres
3.2 the first main theorem
3.3 the second main theorem
4. Nevanlinna Theory of Several Variables
4.1 Biebelbach's example
4.2 the first main theorem
4.3 the second main theorem
4.4 defect relation
4.5 applications
References