Hyperbolic manifolds and holomorphic mappings: an introduction
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New Jersey [u.a.]
World Scientific
2005
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 148 S. |
| ISBN: | 9812564969 9812565892 |
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MARC
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| 245 | 1 | 0 | |a Hyperbolic manifolds and holomorphic mappings |b an introduction |c Shoshichi Kobayashi |
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Record in the Search Index
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| adam_text | CONTENTS
Preface to the New Edition vii
Preface ix
Chapter I The Schwarz Lemma and Its Generalizations 1
1 The Schwarz Pick Lemma 1
2 A Generalization by Ahlfors 3
3 The Gaussian Plane Minus Two Points 5
4 Schottky s Theorem 10
5 Compact Riemann Surfaces of Genus ^2 11
6 Holomorphic Mappings from an Annulus into an Annulus 12
Chapter II Volume Elements and the Schwarz Lemma 16
1 Volume Element and Associated Hermitian Form 17
2 Basic Formula 19
3 Holomorphic Mappings / : M —* M with Compact M 20
4 Holomorphic Mappings /:D M, Where D is a Homogeneous
Bounded Domain 25
5 Affinely Homogeneous Siegel Domains of Second Kind 28
6 Symmetric Bounded Domains 33
Chapter III Distance and the Schwarz Lemma 36
1 Hermitian Vector Bundles and Curvatures 37
2 The Case Where the Domain is a Disk 40
3 The Case Where the Domain is a Polydisk 40
4 The Case Where D is a Symmetric Bounded Domain 41
Chapter IV Invariant Distances on Complex Manifolds 44
1 An Invariant Pseudodistance 45
2 Caratheodory Distance 49
3 Completeness with Respect to the Caratheodory Distance 52
4 Hyperbolic Manifolds 56
5 On Completeness of an Invariant Distance 63
xi
xii Contents
Chapter V Holomorphic Mappings into Hyperbolic Manifolds 67
1 The Little Picard Theorem 67
2 The Automorphism Group of a Hyperbolic Manifold 67
3 Holomorphic Mappings into Hyperbolic Manifolds 70
Chapter VI The Big Picard Theorem and Extension of Holomorphic
Mappings 77
1 Statement of the Problem 77
2 The Invariant Distance on the Punctured Disk 78
3 Mappings from the Punctured Disk into a Hyperbolic Manifold 81
4 Holomorphic Mappings into Compact Hyperbolic Manifolds 84
5 Holomorphic Mappings into Complete Hyperbolic Manifolds 85
6 Holomorphic Mappings into Relatively Compact Hyperbolic
Manifolds 88
Chapter VII Generalization to Complex Spaces 93
1 Complex Spaces 93
2 Invariant Distances for Complex Spaces 95
3 Extension of Mappings into Hyperbolic Spaces 96
4 Normalization of Hyperbolic Complex Spaces 98
5 Complex V Manifolds (Now Called Orbitfolds) 100
6 Invariant Distances on M/V 100
Chapter VIII Hyperbolic Manifolds and Minimal Models 103
1 Meromorphic Mappings 103
2 Strong Minimality and Minimal Models 104
3 Relative Minimality 108
Chapter IX Miscellany 115
1 Invariant Measures 115
2 Intermediate Dimensional Invariant Measures 118
3 Unsolved Problems 125
Postscript 129
Bibliography 135
Summary of Notations 143
Author Index 145
Subject Index 147
|
| adam_txt |
CONTENTS
Preface to the New Edition vii
Preface ix
Chapter I The Schwarz Lemma and Its Generalizations 1
1 The Schwarz Pick Lemma 1
2 A Generalization by Ahlfors 3
3 The Gaussian Plane Minus Two Points 5
4 Schottky's Theorem 10
5 Compact Riemann Surfaces of Genus ^2 11
6 Holomorphic Mappings from an Annulus into an Annulus 12
Chapter II Volume Elements and the Schwarz Lemma 16
1 Volume Element and Associated Hermitian Form 17
2 Basic Formula 19
3 Holomorphic Mappings / : M' —* M with Compact M 20
4 Holomorphic Mappings /:D M, Where D is a Homogeneous
Bounded Domain 25
5 Affinely Homogeneous Siegel Domains of Second Kind 28
6 Symmetric Bounded Domains 33
Chapter III Distance and the Schwarz Lemma 36
1 Hermitian Vector Bundles and Curvatures 37
2 The Case Where the Domain is a Disk 40
3 The Case Where the Domain is a Polydisk 40
4 The Case Where D is a Symmetric Bounded Domain 41
Chapter IV Invariant Distances on Complex Manifolds 44
1 An Invariant Pseudodistance 45
2 Caratheodory Distance 49
3 Completeness with Respect to the Caratheodory Distance 52
4 Hyperbolic Manifolds 56
5 On Completeness of an Invariant Distance 63
xi
xii Contents
Chapter V Holomorphic Mappings into Hyperbolic Manifolds 67
1 The Little Picard Theorem 67
2 The Automorphism Group of a Hyperbolic Manifold 67
3 Holomorphic Mappings into Hyperbolic Manifolds 70
Chapter VI The Big Picard Theorem and Extension of Holomorphic
Mappings 77
1 Statement of the Problem 77
2 The Invariant Distance on the Punctured Disk 78
3 Mappings from the Punctured Disk into a Hyperbolic Manifold 81
4 Holomorphic Mappings into Compact Hyperbolic Manifolds 84
5 Holomorphic Mappings into Complete Hyperbolic Manifolds 85
6 Holomorphic Mappings into Relatively Compact Hyperbolic
Manifolds 88
Chapter VII Generalization to Complex Spaces 93
1 Complex Spaces 93
2 Invariant Distances for Complex Spaces 95
3 Extension of Mappings into Hyperbolic Spaces 96
4 Normalization of Hyperbolic Complex Spaces 98
5 Complex V Manifolds (Now Called Orbitfolds) 100
6 Invariant Distances on M/V 100
Chapter VIII Hyperbolic Manifolds and Minimal Models 103
1 Meromorphic Mappings 103
2 Strong Minimality and Minimal Models 104
3 Relative Minimality 108
Chapter IX Miscellany 115
1 Invariant Measures 115
2 Intermediate Dimensional Invariant Measures 118
3 Unsolved Problems 125
Postscript 129
Bibliography 135
Summary of Notations 143
Author Index 145
Subject Index 147 |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 2. ed. |
| format | Book |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T13:40:19Z |
| indexdate | 2024-07-09T20:33:58Z |
| institution | BVB |
| isbn | 9812564969 9812565892 |
| language | English |
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| physical | XII, 148 S. |
| publishDate | 2005 |
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| publisher | World Scientific |
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| spelling | Kobayashi, Shōshichi 1932-2012 Verfasser (DE-588)107956209 aut Hyperbolic manifolds and holomorphic mappings an introduction Shoshichi Kobayashi 2. ed. New Jersey [u.a.] World Scientific 2005 XII, 148 S. txt rdacontent n rdamedia nc rdacarrier Holomorphe Abbildung - Hyperbolische Mannigfaltigkeit Complex manifolds Holomorphic mappings Hyperbolische Mannigfaltigkeit (DE-588)4161044-1 gnd rswk-swf Holomorphe Abbildung (DE-588)4160471-4 gnd rswk-swf Hyperbolische Mannigfaltigkeit (DE-588)4161044-1 s Holomorphe Abbildung (DE-588)4160471-4 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014576335&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kobayashi, Shōshichi 1932-2012 Hyperbolic manifolds and holomorphic mappings an introduction Holomorphe Abbildung - Hyperbolische Mannigfaltigkeit Complex manifolds Holomorphic mappings Hyperbolische Mannigfaltigkeit (DE-588)4161044-1 gnd Holomorphe Abbildung (DE-588)4160471-4 gnd |
| subject_GND | (DE-588)4161044-1 (DE-588)4160471-4 |
| title | Hyperbolic manifolds and holomorphic mappings an introduction |
| title_auth | Hyperbolic manifolds and holomorphic mappings an introduction |
| title_exact_search | Hyperbolic manifolds and holomorphic mappings an introduction |
| title_exact_search_txtP | Hyperbolic manifolds and holomorphic mappings an introduction |
| title_full | Hyperbolic manifolds and holomorphic mappings an introduction Shoshichi Kobayashi |
| title_fullStr | Hyperbolic manifolds and holomorphic mappings an introduction Shoshichi Kobayashi |
| title_full_unstemmed | Hyperbolic manifolds and holomorphic mappings an introduction Shoshichi Kobayashi |
| title_short | Hyperbolic manifolds and holomorphic mappings |
| title_sort | hyperbolic manifolds and holomorphic mappings an introduction |
| title_sub | an introduction |
| topic | Holomorphe Abbildung - Hyperbolische Mannigfaltigkeit Complex manifolds Holomorphic mappings Hyperbolische Mannigfaltigkeit (DE-588)4161044-1 gnd Holomorphe Abbildung (DE-588)4160471-4 gnd |
| topic_facet | Holomorphe Abbildung - Hyperbolische Mannigfaltigkeit Complex manifolds Holomorphic mappings Hyperbolische Mannigfaltigkeit Holomorphe Abbildung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014576335&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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