Invariant distances and metrics in complex analysis:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin u.a.
de Gruyter
1993
|
| Schriftenreihe: | De Gruyter expositions in mathematics
9 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 408 S. Ill. |
| ISBN: | 3110132516 |
Internformat
MARC
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| 100 | 1 | |a Jarnicki, Marek |d 1952- |e Verfasser |0 (DE-588)101811095X |4 aut | |
| 245 | 1 | 0 | |a Invariant distances and metrics in complex analysis |c by Marek Jarnicki ; Peter Pflug |
| 264 | 1 | |a Berlin u.a. |b de Gruyter |c 1993 | |
| 300 | |a XI, 408 S. |b Ill. | ||
| 336 | |b txt |2 rdacontent | ||
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Datensatz im Suchindex
| _version_ | 1804121742961016832 |
|---|---|
| adam_text | Contents
Preface vii
I Hyperbolic geometry of the unit disc 1
Exercises 14
II The Caratheodory pseudodistance and the Caratheodory Reiffen
pseudometric 15
2.1 Definitions. General Schwarz Pick Lemma 16
2.2 Balanced domains 18
2.3 Caratheodory hyperbolicity 27
2.4 The Caratheodory topology 29
2.5 Properties of c* * 1 and y. Length of curve. Inner Caratheodory
pseudodistance 33
2.6 Two applications 48
2.7 A class of n circled domains 53
Notes 65
Exercises 66
III The Kobayashi pseudodistance and the Kobayashi Royden
pseudometric 71
3.1 The Lempert function and the Kobayashi pseudodistance . . 71
3.2 Tautness 77
3.3 General properties of k 82
3.4 An extension theorem 87
3.5 The Kobayashi Royden pseudometric 90
3.6 The Kobayashi Buseman pseudometric 99
3.7 Product formula 106
Notes 108
Exercises 109
IV Contractible systems Ill
4.1 Abstract point of view Ill
4.2 Extremal problems for plurisubharmonic functions 115
4.3 Inner pseudodistances. Integrated forms. Derivatives.
Buseman pseudometrics. C pseudodistances 139
x Contents
4.4 Example elementary n circled domains 149
Notes 152
Exercises 153
V Contractible functions and metrics for the annulus 154
Notes 165
Exercises 166
VI The Bergman metric 169
6.1 The Bergman kernel 169
6.2 The Bergman pseudometric 185
6.3 Comparison and localization 190
6.4 The Skwarczyriski pseudometric 195
Notes 198
Exercises 200
VII Hyperbolicity and completeness 202
7.1 Global hyperbolicity 202
7.2 Local hyperbolicity 207
7.3 Completeness general discussion 213
7.4 Caratheodory completeness 216
7.5 Kobayashi completeness 223
7.6 Bergman completeness 230
Notes 234
Exercises 235
VIII Complex geodesies. Lempert s theorem 237
8.1 Complex geodesies 237
8.2 Lempert s theorem 243
8.3 Uniqueness of complex geodesies 255
8.4 Geodesies in convex complex ellipsoids 264
8.5 Biholomorphisms of complex ellipsoids 278
8.6 Schwarz Lemma the case of equality 281
8.7 Criteria for biholomorphicity 285
Notes 288
Exercises 290
IX Product property 296
Exercises 309
X Comparison on strongly pseudoconvex domains 310
10.1 Strongly pseudoconvex domains 310
Contents xi
10.2 The boundary behavior of the Caratheodory
and the Kobayashi distances 316
10.3 Localization 326
10.4 Boundary behavior of the Caratheodory Reiffen
and the Kobayashi Royden metrics 331
10.5 A comparison of distances 342
10.6 Characterization of the unit ball by its automorphism group . 344
Notes 352
Exercises 353
Miscellanea 355
A The automorphism group of bounded domains 355
B Holomorphic curvature 356
C Complex geodesies 359
D Criteria for biholomorphicity 361
E Boundary behavior of contractible metrics
on weakly pseudoconvex domains 363
Appendix 367
HF Holomorphic functions 367
PSH Subharmonic and plurisubharmonic functions 370
PSC Domains of holomorphy and pseudoconvex domains .... 375
AUT Automorphisms 379
Automorphisms of the unit disc 379
Automorphisms of the unit polydisc 379
Automorphisms of the unit Euclidean ball 380
GR Green function and Dirichlet problem 380
MA Monge Ampere operator 383
H Hardy spaces 384
References 387
List of symbols 400
Index 405
|
| any_adam_object | 1 |
| author | Jarnicki, Marek 1952- Pflug, Peter |
| author_GND | (DE-588)101811095X |
| author_facet | Jarnicki, Marek 1952- Pflug, Peter |
| author_role | aut aut |
| author_sort | Jarnicki, Marek 1952- |
| author_variant | m j mj p p pp |
| building | Verbundindex |
| bvnumber | BV007466681 |
| classification_rvk | SK 280 SK 700 SK 750 SK 780 |
| classification_tum | MAT 329f MAT 303f |
| ctrlnum | (OCoLC)246790278 (DE-599)BVBBV007466681 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV007466681 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:02:49Z |
| institution | BVB |
| isbn | 3110132516 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-004847173 |
| oclc_num | 246790278 |
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| physical | XI, 408 S. Ill. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | de Gruyter |
| record_format | marc |
| series | De Gruyter expositions in mathematics |
| series2 | De Gruyter expositions in mathematics |
| spelling | Jarnicki, Marek 1952- Verfasser (DE-588)101811095X aut Invariant distances and metrics in complex analysis by Marek Jarnicki ; Peter Pflug Berlin u.a. de Gruyter 1993 XI, 408 S. Ill. txt rdacontent n rdamedia nc rdacarrier De Gruyter expositions in mathematics 9 Invariante - Metrischer Raum - Pseudometrik Komplexe Funktion (DE-588)4217733-9 gnd rswk-swf Pseudoabstand (DE-588)4335987-5 gnd rswk-swf Pseudometrik (DE-588)4176150-9 gnd rswk-swf Metrischer Raum (DE-588)4169745-5 gnd rswk-swf Invariante (DE-588)4128781-2 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Komplexe Funktion (DE-588)4217733-9 s Pseudoabstand (DE-588)4335987-5 s Invariante (DE-588)4128781-2 s Metrischer Raum (DE-588)4169745-5 s DE-604 Funktionentheorie (DE-588)4018935-1 s Pseudometrik (DE-588)4176150-9 s 1\p DE-604 Pflug, Peter Verfasser aut De Gruyter expositions in mathematics 9 (DE-604)BV004069300 9 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004847173&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Jarnicki, Marek 1952- Pflug, Peter Invariant distances and metrics in complex analysis De Gruyter expositions in mathematics Invariante - Metrischer Raum - Pseudometrik Komplexe Funktion (DE-588)4217733-9 gnd Pseudoabstand (DE-588)4335987-5 gnd Pseudometrik (DE-588)4176150-9 gnd Metrischer Raum (DE-588)4169745-5 gnd Invariante (DE-588)4128781-2 gnd Funktionentheorie (DE-588)4018935-1 gnd |
| subject_GND | (DE-588)4217733-9 (DE-588)4335987-5 (DE-588)4176150-9 (DE-588)4169745-5 (DE-588)4128781-2 (DE-588)4018935-1 |
| title | Invariant distances and metrics in complex analysis |
| title_auth | Invariant distances and metrics in complex analysis |
| title_exact_search | Invariant distances and metrics in complex analysis |
| title_full | Invariant distances and metrics in complex analysis by Marek Jarnicki ; Peter Pflug |
| title_fullStr | Invariant distances and metrics in complex analysis by Marek Jarnicki ; Peter Pflug |
| title_full_unstemmed | Invariant distances and metrics in complex analysis by Marek Jarnicki ; Peter Pflug |
| title_short | Invariant distances and metrics in complex analysis |
| title_sort | invariant distances and metrics in complex analysis |
| topic | Invariante - Metrischer Raum - Pseudometrik Komplexe Funktion (DE-588)4217733-9 gnd Pseudoabstand (DE-588)4335987-5 gnd Pseudometrik (DE-588)4176150-9 gnd Metrischer Raum (DE-588)4169745-5 gnd Invariante (DE-588)4128781-2 gnd Funktionentheorie (DE-588)4018935-1 gnd |
| topic_facet | Invariante - Metrischer Raum - Pseudometrik Komplexe Funktion Pseudoabstand Pseudometrik Metrischer Raum Invariante Funktionentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004847173&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004069300 |
| work_keys_str_mv | AT jarnickimarek invariantdistancesandmetricsincomplexanalysis AT pflugpeter invariantdistancesandmetricsincomplexanalysis |