Conformal invariants: topics in geometric function theory
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY [u.a.]
McGraw-Hill Book Company
1973
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| Series: | McGraw-Hill Series in Higher Mathematics
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VII, 157 Seiten graph. Darst. |
| ISBN: | 0070006598 |
Staff View
MARC
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| 100 | 1 | |a Ahlfors, Lars Valerian |d 1907-1996 |e Verfasser |0 (DE-588)104541164 |4 aut | |
| 245 | 1 | 0 | |a Conformal invariants |b topics in geometric function theory |c Lars V. Ahlfors, Professor of Mathematics, Harvard University |
| 264 | 1 | |a New York, NY [u.a.] |b McGraw-Hill Book Company |c 1973 | |
| 300 | |a VII, 157 Seiten |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a McGraw-Hill Series in Higher Mathematics | |
| 650 | 4 | |a Fonctions d'une variable complexe | |
| 650 | 7 | |a Fonctions, théorie géométrique des |2 ram | |
| 650 | 4 | |a Invariants conformes | |
| 650 | 7 | |a Invariants conformes |2 ram | |
| 650 | 4 | |a Riemann, Surfaces de | |
| 650 | 7 | |a Riemann, surfaces de |2 ram | |
| 650 | 4 | |a Conformal invariants | |
| 650 | 4 | |a Geometric function theory | |
| 650 | 4 | |a Riemann surfaces | |
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Record in the Search Index
| _version_ | 1804117098511728640 |
|---|---|
| adam_text | Contents
Preface ix
1. Applications of Schwarz s lemma 1
1 1. The noneuclidean metric 1
1 2. The Schwarz Pick theorem 3
1 3. Convex regions 5
1 4. Angular derivatives 7
1 5. Ultrahyperbolic metrics 12
1 6. Bloch s theorem 14
1 7. The Poincare metric of a region 16
1 8. An elementary lower bound 16
1 9. The Picard theorems 19
2. Capacity 23
2 1. The transfinite diameter 23
2 2. Potentials 24
2 3. Capacity and the transfinite diameter 27
2 4. Subsets of a circle 30
2 5. Symmetrization 31
3. Harmonic measure 37
3 1. The majorization principle 37
3 2. Applications in a half plane *
3 3. Milloux s problem
3 4. The precise form of Hadamard s theorem 44
4. Extremal length 50
4 1. Definition of extremal length 50
4 2. Examples 52
4 3. The comparison principle
vi CONTENTS
4 4. The composition laws 54
4 5. An integral inequality 56
4 6. Prime ends 57
4 7. Extremal metrics 61
4 8. A case of spherical extremal metric 63
4 9. The explicit formula for extremal distance 65
4 10. Configurations with a single modulus 70
4 11. Extremal annuli 71
4 12. The function A(R) 74
4 13. A distortion theorem 76
4 14. Reduced extremal distance 78
5. Elementary theory of univalent functions 82
5 1. The area theorem 82
5 2. The Grunsky and Golusin inequalities 85
5 3. Proof of |o4| 4 87
6. Loewner s method 92
6 1. Approximation by slit mappings 92
6 2. Loewner s differential equation 96
6 3. Proof of a, 3 96
7. The Schiffer variation 98
7 1. Variation of the Green s function 98
7 2. Variation of the mapping function 102
7 3. The final theorem 105
7 4. The slit variation 106
8. Properties of the extremal functions 107
8 1. The differential equation 107
8 2. Trajectories 110
8 3. The r structures 114
CONTKNTS vii
8 4. Regularity and global correspondence 116
8 5. The case n = 3 118
9. Riemann surfaces 125
9 1. Definition and examples 125
9 2. Covering surfaces 127
9 3. The fundamental group 128
9 4. Subgroups and covering surfaces 130
9 5. Cover transformations 132
9 6. Simply connected surfaces 134
10. The uniformization theorem 136
10 1. Existence of the Green s function 136
10 2. Harmonic measure and the maximum principle 138
10 3. Equivalence of the basic conditions 139
10 4. Proof of the uniformization theorem (Part I) 142
10 5. Proof of the uniformization theorem (Part II) 147
10 6. Arbitrary Riemann surfaces 149
Bibliography 152
Index 156
|
| any_adam_object | 1 |
| author | Ahlfors, Lars Valerian 1907-1996 |
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| author_facet | Ahlfors, Lars Valerian 1907-1996 |
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| ctrlnum | (OCoLC)572899 (DE-599)BVBBV002745267 |
| 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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| illustrated | Illustrated |
| indexdate | 2024-07-09T15:49:00Z |
| institution | BVB |
| isbn | 0070006598 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001755303 |
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| physical | VII, 157 Seiten graph. Darst. |
| publishDate | 1973 |
| publishDateSearch | 1973 |
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| publisher | McGraw-Hill Book Company |
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| series2 | McGraw-Hill Series in Higher Mathematics |
| spelling | Ahlfors, Lars Valerian 1907-1996 Verfasser (DE-588)104541164 aut Conformal invariants topics in geometric function theory Lars V. Ahlfors, Professor of Mathematics, Harvard University New York, NY [u.a.] McGraw-Hill Book Company 1973 VII, 157 Seiten graph. Darst. txt rdacontent n rdamedia nc rdacarrier McGraw-Hill Series in Higher Mathematics Fonctions d'une variable complexe Fonctions, théorie géométrique des ram Invariants conformes Invariants conformes ram Riemann, Surfaces de Riemann, surfaces de ram Conformal invariants Geometric function theory Riemann surfaces Konforme Invariante (DE-588)4320354-1 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Riemannsche Fläche (DE-588)4049991-1 gnd rswk-swf Riemannsche Fläche (DE-588)4049991-1 s DE-604 Konforme Invariante (DE-588)4320354-1 s Funktionentheorie (DE-588)4018935-1 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001755303&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ahlfors, Lars Valerian 1907-1996 Conformal invariants topics in geometric function theory Fonctions d'une variable complexe Fonctions, théorie géométrique des ram Invariants conformes Invariants conformes ram Riemann, Surfaces de Riemann, surfaces de ram Conformal invariants Geometric function theory Riemann surfaces Konforme Invariante (DE-588)4320354-1 gnd Funktionentheorie (DE-588)4018935-1 gnd Riemannsche Fläche (DE-588)4049991-1 gnd |
| subject_GND | (DE-588)4320354-1 (DE-588)4018935-1 (DE-588)4049991-1 |
| title | Conformal invariants topics in geometric function theory |
| title_auth | Conformal invariants topics in geometric function theory |
| title_exact_search | Conformal invariants topics in geometric function theory |
| title_full | Conformal invariants topics in geometric function theory Lars V. Ahlfors, Professor of Mathematics, Harvard University |
| title_fullStr | Conformal invariants topics in geometric function theory Lars V. Ahlfors, Professor of Mathematics, Harvard University |
| title_full_unstemmed | Conformal invariants topics in geometric function theory Lars V. Ahlfors, Professor of Mathematics, Harvard University |
| title_short | Conformal invariants |
| title_sort | conformal invariants topics in geometric function theory |
| title_sub | topics in geometric function theory |
| topic | Fonctions d'une variable complexe Fonctions, théorie géométrique des ram Invariants conformes Invariants conformes ram Riemann, Surfaces de Riemann, surfaces de ram Conformal invariants Geometric function theory Riemann surfaces Konforme Invariante (DE-588)4320354-1 gnd Funktionentheorie (DE-588)4018935-1 gnd Riemannsche Fläche (DE-588)4049991-1 gnd |
| topic_facet | Fonctions d'une variable complexe Fonctions, théorie géométrique des Invariants conformes Riemann, Surfaces de Riemann, surfaces de Conformal invariants Geometric function theory Riemann surfaces Konforme Invariante Funktionentheorie Riemannsche Fläche |
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