Geometric Function Theory in Several Complex VariablesThis is an expanded English-language version of a book by the same authors that originally appeared in the Japanese. The book serves two purposes. The first is to provide a self-contained and coherent account of recent developments in geometric function theory in several complex variables, aimed at those who have already mastered the basics of complex function theory and the elementary theory of differential and complex manifolds. The second goal is to present, in a self-contained way, fundamental descriptions of the theory of positive currents, plurisubharmonic functions, and meromorphic mappings, which are today indispensable in the analytic and geometric theories of complex functions of several variables. The book should prove useful for researchers and graduate students alike. |
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Contents
Hyperbolic Manifolds | 1 |
12 Kobayashi Differential Metric | 4 |
13 Kobayashi PseudoDistance | 11 |
14 The Original Definition of the Kobayashi PseudoDistance | 16 |
15 General Properties of Hyperbolic Manifolds | 18 |
16 Holomorphic Mappings into Hyperbolic Manifolds | 26 |
17 Function Theoretic Criterion of Hyperbolicity | 36 |
18 Holomorphic Mappings Omitting Hypersurfaces | 39 |
32 Positive Currents | 108 |
33 Plurisubharmonic Functions | 121 |
Meromorphic Mappings | 139 |
42 Divisors and Meromorphic Functions | 143 |
43 Holomorphic Mappings | 151 |
44 Meromorphic Mappings | 152 |
45 Meromorphic Functions and Meromorphic Mappings | 160 |
Nevanlinna Theory | 167 |
19 Geometric Criterion of Complete Hyperbolicity | 47 |
110 Existence of a Rotationally Symmetric Hermitian Metric | 51 |
Measure Hyperbolic Manifolds | 59 |
22 PseudoVolume Elements and Ricci Curiature Functions | 73 |
23 Hyperbolic PseudoVolume Form | 77 |
24 Measure Hyperbolic Manifolds | 79 |
25 Differential Geometric Criterion of Measure Hyperbolicity | 82 |
26 Meromorphic Mappings into a Measure Hyperbolic Manifold | 83 |
Currents and Plurisubharmonic Functions | 93 |
52 Characteristic Functions and the First Main Theorem | 177 |
53 Elementary Properties of Characteristic Functions | 188 |
54 CasoratiWeierstrass Theorem | 197 |
55 The Second Main Theorem | 201 |
Value Distribution of Holomorphic Curves | 221 |
62 Elementary Facts on Algebraic Varieties | 231 |
63 Jet Bundles and Subvarieties of Abelian Varieties | 237 |
64 Hindis Conjecture | 242 |
Other editions - View all
Geometric Function Theory in Several Complex Variables Junjirō Noguchi,Kikagakuteki Kansuron,Takushiro Ochiai,T. Ochiai No preview available - 1990 |
Geometric Function Theory in Several Complex Variables Junjirō Noguchi,Takushiro Ochiai No preview available - 1990 |
Common terms and phrases
algebraic variety analytic hypersurface analytic subset assume biholomorphic called Chapter clear closed compact compact subset complex manifold component connected consider contains continuous converges coordinate system Corollary covering define definition denote differential dimension distribution divisor element equivalence Example exists extended fact finite follows follows from Theorem give hand Hence hermitian metric holds holo holomorphic function holomorphic line bundle holomorphic local coordinate holomorphic mapping hyperbolic manifold implies independent integrable irreducible Kobayashi Lemma linear m-dimensional meromorphic function meromorphic mapping Moreover natural neighborhood non-degenerate Note obtain open subset origin plurisubharmonic functions polynomial positive positive current Proof proper Proposition proved rank rational Remark resp respect satisfies sequence sufficient supp Suppose Take Theorem theory trivialization uniquely vector space volume write Zero
Bibliographic information
| Title | Geometric Function Theory in Several Complex Variables Issue 80 of Translations of mathematical monographs, ISSN 0065-9282 |
| Authors | Junjirō Noguchi, Kikagakuteki Kansuron, Takushiro Ochiai, T. Ochiai |
| Edition | reprint |
| Publisher | American Mathematical Soc., 1990 |
| ISBN | 0821845330, 9780821845332 |
| Length | 282 pages |
| Subjects | › Mathematics / General |
| Export Citation | BiBTeX EndNote RefMan |