Hyperbolic Complex Spaces

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Springer Science & Business Media, Mar 9, 2013 - Mathematics - 474 pages
In the three decades since the introduction of the Kobayashi distance, the subject of hyperbolic complex spaces and holomorphic mappings has grown to be a big industry. This book gives a comprehensive and systematic account on the Carathéodory and Kobayashi distances, hyperbolic complex spaces and holomorphic mappings with geometric methods. A very complete list of references should be useful for prospective researchers in this area.
 

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Contents

Degeneracy of Inner Pseudodistances
2
Norms and Indicatrices
13
Two Intrinsic Pseudodistances
48
Hyperbolicity
60
Hyperbolic Imbeddings
70
Relative Intrinsic Pseudodistance
80
Infinitesimal Pseudometric
100
Differential Geometric Criteria for Hyperbolicity
112
Holomorphic Maps into Hyperbolic Spaces
238
Extension and Finiteness Theorems
277
Complex Finsler Vector Bundles
335
Manifolds of General Type
342
19
389
Value Distributions
393
30
403
35
413

Theorem of BlochOchiai
124
Projective Spaces with Hyperplanes Deleted
134
Deformations and Hyperbolicity
148
NevanlinnaCartan Theory
159

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