The Schwarz lemma:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Clarendon Press
1989
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| Series: | Oxford Mathematical Monographs
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 248 Seiten |
| ISBN: | 0198535716 |
Staff View
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
PART I
1. The classical Schwarz lemma 3
1.1 The Schwarz lemma and the Schwarz Pick lemma 4
1.2 A Schwarz lemma for subharmonic functions 10
Notes and remarks 16
2. A Schwarz lemma for plurisubharmonic functions 20
2.1 Potential theory on R and C 20
2.2 A Schwarz lemma for plurisubharmonic functions 27
Notes and remarks 31
3. The Poincare distance on the unit disc 33
3.1 Introduction 33
3.2 The Poincare distance on the unit disc 35
3.3 Infinitesimal Finsler pseudometrics 40
3.4 Holomorphic curvature (1) 43
3.5 The Poincare distance and the Green function on D 45
Notes and remarks 45
4. Schwarz Pick systems of pseudodistances 47
4.1 Schwarz Pick systems 47
4.2 The infinitesimal Caratheodory and Kobayashi
pseudometrics 54
Notes and remarks 68
5. Hyperbolic manifolds 71
5.1 Extension theorems 72
5.2 Equicontinuous families of holomorphic mappings 77
Notes and remarks 80
6. Special domains 82
6.1 Balanced pseudoconvex domains 83
6.2 Convex domains 87
6.3 A characterization of the polydisc 97
Notes and remarks 103
x The Schwarz lemma
7. Pseudometrics defined using the (complex) Green
function 107
7.1 Inequalities satisfied by the (complex) Green function 107
7.2 The infinitesimal pseudometrics of Sibony and Azukawa 112
7.3 Infinitesimal metrics on the annulus 119
Notes and remarks 125
8. Holomorphic curvature 126
8.1 Curvature in differential geometry 126
8.2 Holomorphic curvature (2) 133
8.3 The Ahlfors Schwarz lemma 135
8.4 Convex domains in the complex plane 141
Notes and remarks 147
9. The algebraic metric of Harris 149
9.1 Bounded symmetric domains and JB* triple systems 149
9.2 The algebraic inner product 157
9.3 The infinitesimal algebraic metric 165
Notes and remarks 169
PART II
10. A holomorphic characterization of Banach spaces
containing Co. 173
10.1 Banach spaces containing cq 173
10.2 Irreducibility and cotype 185
Notes and remarks 190
11. Fixed point theorems 191
11.1 The Earle Hamilton fixed point theorem 192
11.2 A fixed point free Schwarz lemma 193
11.3 Holomorphic retracts 203
Notes and remarks 211
12. The analytic Radon Nikodym property 213
12.1 Closed bounded submanifolds 213
12.2 Geometric properties of Banach spaces 214
12.3 Caratheodory complete complex Banach manifolds 217
Notes and remarks 219
References 221
Index 241
|
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| ctrlnum | (OCoLC)246667885 (DE-599)BVBBV002501628 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV002501628 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:45:58Z |
| institution | BVB |
| isbn | 0198535716 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001611498 |
| oclc_num | 246667885 |
| open_access_boolean | |
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| owner_facet | DE-12 DE-91G DE-BY-TUM DE-739 DE-355 DE-BY-UBR DE-29T DE-19 DE-BY-UBM DE-706 DE-11 DE-188 |
| physical | X, 248 Seiten |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | Clarendon Press |
| record_format | marc |
| series2 | Oxford Mathematical Monographs |
| spelling | Dineen, Seán 1944- Verfasser (DE-588)115656715 aut The Schwarz lemma Seán Dineen, University College Dublin Oxford Clarendon Press 1989 X, 248 Seiten txt rdacontent n rdamedia nc rdacarrier Oxford Mathematical Monographs Schwarzsches Lemma (DE-588)4180365-6 gnd rswk-swf Subharmonische Funktion (DE-588)4183900-6 gnd rswk-swf Schwarzsches Lemma (DE-588)4180365-6 s DE-604 Subharmonische Funktion (DE-588)4183900-6 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001611498&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dineen, Seán 1944- The Schwarz lemma Schwarzsches Lemma (DE-588)4180365-6 gnd Subharmonische Funktion (DE-588)4183900-6 gnd |
| subject_GND | (DE-588)4180365-6 (DE-588)4183900-6 |
| title | The Schwarz lemma |
| title_auth | The Schwarz lemma |
| title_exact_search | The Schwarz lemma |
| title_full | The Schwarz lemma Seán Dineen, University College Dublin |
| title_fullStr | The Schwarz lemma Seán Dineen, University College Dublin |
| title_full_unstemmed | The Schwarz lemma Seán Dineen, University College Dublin |
| title_short | The Schwarz lemma |
| title_sort | the schwarz lemma |
| topic | Schwarzsches Lemma (DE-588)4180365-6 gnd Subharmonische Funktion (DE-588)4183900-6 gnd |
| topic_facet | Schwarzsches Lemma Subharmonische Funktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001611498&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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