Boundary behaviour of conformal maps:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1992
|
| Schriftenreihe: | Die Grundlehren der mathematischen Wissenschaften
299 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 300 S. graph. Darst. |
| ISBN: | 9783642081293 3540547517 0387547517 |
Internformat
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| 100 | 1 | |a Pommerenke, Christian |d 1933-2024 |e Verfasser |0 (DE-588)1102930121 |4 aut | |
| 245 | 1 | 0 | |a Boundary behaviour of conformal maps |c Ch. Pommerenke |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1992 | |
| 300 | |a IX, 300 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Grundlehren der mathematischen Wissenschaften |v 299 | |
| 650 | 4 | |a Applications conformes | |
| 650 | 4 | |a Problèmes aux limites | |
| 650 | 4 | |a Boundary value problems | |
| 650 | 4 | |a Conformal mapping | |
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Datensatz im Suchindex
| _version_ | 1808949650645843968 |
|---|---|
| adam_text |
Contents
Chapter 1. Some Basic Facts 1
1.1 Sets and Curves 1
1.2 Conformal Maps 4
1.3 The Koebe Distortion Theorem 8
1.4 Sequences of Conformal Maps 13
1.5 Some Univalence Criteria 15
Chapter 2. Continuity and Prime Ends 18
2.1 An Overview 18
2.2 Local Connection 19
2.3 Cut Points and Jordan Domains 23
2.4 Crosscuts and Prime Ends 27
2.5 Limits and Cluster Sets 32
2.6 Countability Theorems 36
Chapter 3. Smoothness and Corners 41
3.1 Introduction 41
3.2 Smooth Jordan Curves 43
3.3 The Continuity of Derivatives 46
3.4 Tangents and Corners 51
3.5 Regulated Domains 59
3.6 Starlike and Close to Convex Domains 65
Chapter 4. Distortion 71
4.1 An Overview 71
4.2 Bloch Functions 72
4.3 The Angular Derivative 79
4.4 Harmonic Measure 84
4.5 Length Distortion 87
4.6 The Hyperbolic Metric 90
VIII Contents
Chapter 5. Quasidisks 94
5.1 An Overview 94
5.2 John Domains 96
5.3 Linearly Connected Domains 103
5.4 Quasidisks and Quasisymmetric Functions 107
5.5 Quasiconformal Extension 112
5.6 Analytic Families of Injections 120
Chapter 6. Linear Measure 126
6.1 An Overview 126
6.2 Linear Measure and Measurability 128
6.3 Rectifiable Curves 134
6.4 Plessner's Theorem and Twisting 139
6.5 Sectorial Accessibility 144
6.6 Jordan Curves and Harmonic Measure 151
Chapter 7. Smirnov and Lavrentiev Domains 155
7.1 An Overview 155
7.2 Integrals of Bloch Functions 156
7.3 Smirnov Domains and Ahlfors Regularity 159
7.4 Lavrentiev Domains 163
7.5 The Muckenhoupt Conditions and BMOA 168
Chapter 8. Integral Means 173
8.1 An Overview 173
8.2 Univalent Functions 174
8.3 Derivatives of Univalent Functions 176
8.4 Coefficient Problems 183
8.5 The Growth of Bloch Functions 185
8.6 Lacunary Series 188
Chapter 9. Curve Families and Capacity 195
9.1 An Overview 195
9.2 The Module of a Curve Family 196
9.3 Capacity and Green's Function 203
9.4 Pfluger's Theorem 210
9.5 Applications to Conformal Mapping 215
Chapter 10. Hausdorff Measure 222
10.1 An Overview 222
10.2 Hausdorff Measures 223
Contents IX
10.3 Lower Bounds for Compression 229
10.4 Zygmund Measures and the Angular Derivative 235
10.5 The Size of the Boundary 240
Chapter 11. Local Boundary Behaviour 245
11.1 An Overview 245
11.2 Asymptotically Conformal Curves and Bo 246
11.3 The Visser Ostrowski Quotient 251
11.4 Module and Conformality 256
11.5 The Ahlfors Integral 263
References 269
Author Index 291
Subject Index 295 |
| any_adam_object | 1 |
| author | Pommerenke, Christian 1933-2024 |
| author_GND | (DE-588)1102930121 |
| author_facet | Pommerenke, Christian 1933-2024 |
| author_role | aut |
| author_sort | Pommerenke, Christian 1933-2024 |
| author_variant | c p cp |
| building | Verbundindex |
| bvnumber | BV005445357 |
| callnumber-first | Q - Science |
| callnumber-label | QA360 |
| callnumber-raw | QA360 |
| callnumber-search | QA360 |
| callnumber-sort | QA 3360 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 380 SK 750 |
| classification_tum | MAT 303f |
| ctrlnum | (OCoLC)25632971 (DE-599)BVBBV005445357 |
| dewey-full | 515/.9 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.9 |
| dewey-search | 515/.9 |
| dewey-sort | 3515 19 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV005445357 |
| illustrated | Illustrated |
| indexdate | 2024-09-01T00:00:21Z |
| institution | BVB |
| isbn | 9783642081293 3540547517 0387547517 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003407035 |
| oclc_num | 25632971 |
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| physical | IX, 300 S. graph. Darst. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Springer |
| record_format | marc |
| series | Die Grundlehren der mathematischen Wissenschaften |
| series2 | Grundlehren der mathematischen Wissenschaften |
| spelling | Pommerenke, Christian 1933-2024 Verfasser (DE-588)1102930121 aut Boundary behaviour of conformal maps Ch. Pommerenke Berlin [u.a.] Springer 1992 IX, 300 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Grundlehren der mathematischen Wissenschaften 299 Applications conformes Problèmes aux limites Boundary value problems Conformal mapping Randverhalten (DE-588)4300459-3 gnd rswk-swf Randwertproblem (DE-588)4048395-2 gnd rswk-swf Grenzwert (DE-588)4129627-8 gnd rswk-swf Konforme Abbildung (DE-588)4164968-0 gnd rswk-swf Konforme Abbildung (DE-588)4164968-0 s Randwertproblem (DE-588)4048395-2 s DE-604 Randverhalten (DE-588)4300459-3 s Grenzwert (DE-588)4129627-8 s Erscheint auch als Online-Ausgabe 978-3-662-02770-7 Die Grundlehren der mathematischen Wissenschaften 299 (DE-604)BV000000395 299 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003407035&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pommerenke, Christian 1933-2024 Boundary behaviour of conformal maps Die Grundlehren der mathematischen Wissenschaften Applications conformes Problèmes aux limites Boundary value problems Conformal mapping Randverhalten (DE-588)4300459-3 gnd Randwertproblem (DE-588)4048395-2 gnd Grenzwert (DE-588)4129627-8 gnd Konforme Abbildung (DE-588)4164968-0 gnd |
| subject_GND | (DE-588)4300459-3 (DE-588)4048395-2 (DE-588)4129627-8 (DE-588)4164968-0 |
| title | Boundary behaviour of conformal maps |
| title_auth | Boundary behaviour of conformal maps |
| title_exact_search | Boundary behaviour of conformal maps |
| title_full | Boundary behaviour of conformal maps Ch. Pommerenke |
| title_fullStr | Boundary behaviour of conformal maps Ch. Pommerenke |
| title_full_unstemmed | Boundary behaviour of conformal maps Ch. Pommerenke |
| title_short | Boundary behaviour of conformal maps |
| title_sort | boundary behaviour of conformal maps |
| topic | Applications conformes Problèmes aux limites Boundary value problems Conformal mapping Randverhalten (DE-588)4300459-3 gnd Randwertproblem (DE-588)4048395-2 gnd Grenzwert (DE-588)4129627-8 gnd Konforme Abbildung (DE-588)4164968-0 gnd |
| topic_facet | Applications conformes Problèmes aux limites Boundary value problems Conformal mapping Randverhalten Randwertproblem Grenzwert Konforme Abbildung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003407035&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000395 |
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