Geometric function theory in several complex variables:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Mathematical Soc.
2008
|
| Edition: | Reprinted with corr., [Nachdr.] |
| Series: | Translations of mathematical monographs
80 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Japan. übers. |
| Physical Description: | XI, 282 S. |
| ISBN: | 0821845330 |
Staff View
MARC
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| 245 | 1 | 0 | |a Geometric function theory in several complex variables |c Junjiro Noguchi ; Takushiro Ochiai |
| 250 | |a Reprinted with corr., [Nachdr.] | ||
| 264 | 1 | |a Providence, RI |b American Mathematical Soc. |c 2008 | |
| 300 | |a XI, 282 S. | ||
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Record in the Search Index
| _version_ | 1804141184346488832 |
|---|---|
| adam_text | Table
of
Contents
Foreword
............................................................................................................
v
Remarks and Notation
....................................................................................... xi
Chapter I Hyperbolic Manifolds
....................................................................... 1
1.1
Geometry on Discs
.................................................................................. 1
1.2
Kobayashi Differential Metric
................................................................. 4
1.3
Kobayashi Pseudo-Distance
.................................................................... 11
1.4
The Original Definition of the Kobayashi Pseudo-Distance
................... 16
1.5
General Properties of Hyperbolic Manifolds
.......................................... 18
1.6
Holomorphic Mappings into Hyperbolic Manifolds
............................... 26
1.7
Function Theoretic Criterion of
Hyperbolicky
........................................ 36
1.8
Holomorphic Mappings Omitting Hypersurfaces
................................... 39
1.9
Geometric Criterion of Complete
Hyperbolicky
..................................... 47
1.10
Existence of a Rotationally Symmetric Hermitian Metric
.................... 51
Notes
.............................................................................................................. 57
Chapter II Measure Hyperbolic Manifolds
....................................................... 59
2.1
Holomorphic Line Bundles and Chern Forms
......................................... 59
Note
................................................................................................................ 72
2.2
Pseudo-
Volume Elements and
Ricci
Curvature Functions
...................... 73
2.3
Hyperbolic
Pseudo-
Volume Form
........................................................... 77
2.4
Measure Hyperbolic Manifolds
............................................................... 79
2.5
Differential Geometric Criterion of Measure Hyperbolicity
................... 82
2.6
Meromorphic Mappings into a Measure Hyperbolic Manifold
.............. 83
Notes
.............................................................................................................. 90
Chapter III Currents and Plurisubharmonic Functions
..................................... 93
3.1
Currents
..................................................................................................... 93
3.2
Positive Currents
...................................................................................... 108
3.3
Plurisubharmonic Functions
.................................................................... 121
Notes
.............................................................................................................. 138
Chapter IV Meromorphic Mappings
................................................................ 139
4.1
Analytic Subsets
...................................................................................... 139
4.2 Divisors
and Meromorphic Functions
..................................................... 143
4.3 Holomorphic
Mappings
........................................................................... 151
4.4 Meromorphic
Mappings
.......................................................................... 152
4.5 Meromorphic
Functions and Meromorphic Mappings
............................ 160
Notes
.............................................................................................................. 166
Chapter V Nevanlinna Theory
.......................................................................... 167
5.1
Poincare -Lelong Formula
........................................................................ 167
5.2
Characteristic Functions and the First Main Theorem
............................ 177
5.3
Elementary Properties of Characteristic Functions
................................. 188
5.4
Casorati-
Weierstrass
Theorem
............................................................... 197
5.5
The Second Main Theorem
..................................................................... 201
Notes
.............................................................................................................. 218
Chapter VI Value Distribution of Holomorphic Curves
.................................. 221
6.1
Preparation from Function Theory in One Complex Variable
................ 221
6.2
Elementary Facts on Algebraic Varieties
................................................ 231
6.3
Jet Bundles and Subvarieties of Abelian Varieties
.................................. 237
6.4
Bloch s Conjecture
.................................................................................. 242
Notes
.............................................................................................................. 246
Appendix I Canonical Bundles of Complex Submanifolds of Pm(C)
.............. 249
Appendix II Weierstrass-Stoll Canonical Functions
........................................ 253
Notes
.................................................................................................................. 266
Bibliography
...................................................................................................... 267
Index
..:............................................................................................................... 275
Symbols
............................................................................................................. 279
|
| any_adam_object | 1 |
| author | Noguchi, Junjiro 1948- Ochiai, Takushiro |
| author_GND | (DE-588)172286816 |
| author_facet | Noguchi, Junjiro 1948- Ochiai, Takushiro |
| author_role | aut aut |
| author_sort | Noguchi, Junjiro 1948- |
| author_variant | j n jn t o to |
| building | Verbundindex |
| bvnumber | BV036109587 |
| classification_rvk | SK 780 |
| classification_tum | MAT 320f |
| ctrlnum | (OCoLC)634350861 (DE-599)BVBBV036109587 |
| discipline | Mathematik |
| edition | Reprinted with corr., [Nachdr.] |
| format | Book |
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| id | DE-604.BV036109587 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:11:50Z |
| institution | BVB |
| isbn | 0821845330 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018999795 |
| oclc_num | 634350861 |
| open_access_boolean | |
| owner | DE-739 |
| owner_facet | DE-739 |
| physical | XI, 282 S. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | American Mathematical Soc. |
| record_format | marc |
| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spelling | Noguchi, Junjiro 1948- Verfasser (DE-588)172286816 aut Kikagakuteki kansūron Geometric function theory in several complex variables Junjiro Noguchi ; Takushiro Ochiai Reprinted with corr., [Nachdr.] Providence, RI American Mathematical Soc. 2008 XI, 282 S. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 80 Aus dem Japan. übers. Riemannscher Raum (DE-588)4128295-4 gnd rswk-swf Mehrere komplexe Variable (DE-588)4169285-8 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Geometrische Funktionentheorie (DE-588)4156711-0 gnd rswk-swf Geometrische Funktionentheorie (DE-588)4156711-0 s Mehrere komplexe Variable (DE-588)4169285-8 s DE-604 Funktionentheorie (DE-588)4018935-1 s Riemannscher Raum (DE-588)4128295-4 s Ochiai, Takushiro Verfasser aut Translations of mathematical monographs 80 (DE-604)BV000002394 80 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018999795&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Noguchi, Junjiro 1948- Ochiai, Takushiro Geometric function theory in several complex variables Translations of mathematical monographs Riemannscher Raum (DE-588)4128295-4 gnd Mehrere komplexe Variable (DE-588)4169285-8 gnd Funktionentheorie (DE-588)4018935-1 gnd Geometrische Funktionentheorie (DE-588)4156711-0 gnd |
| subject_GND | (DE-588)4128295-4 (DE-588)4169285-8 (DE-588)4018935-1 (DE-588)4156711-0 |
| title | Geometric function theory in several complex variables |
| title_alt | Kikagakuteki kansūron |
| title_auth | Geometric function theory in several complex variables |
| title_exact_search | Geometric function theory in several complex variables |
| title_full | Geometric function theory in several complex variables Junjiro Noguchi ; Takushiro Ochiai |
| title_fullStr | Geometric function theory in several complex variables Junjiro Noguchi ; Takushiro Ochiai |
| title_full_unstemmed | Geometric function theory in several complex variables Junjiro Noguchi ; Takushiro Ochiai |
| title_short | Geometric function theory in several complex variables |
| title_sort | geometric function theory in several complex variables |
| topic | Riemannscher Raum (DE-588)4128295-4 gnd Mehrere komplexe Variable (DE-588)4169285-8 gnd Funktionentheorie (DE-588)4018935-1 gnd Geometrische Funktionentheorie (DE-588)4156711-0 gnd |
| topic_facet | Riemannscher Raum Mehrere komplexe Variable Funktionentheorie Geometrische Funktionentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018999795&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000002394 |
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