Teichmüller theory and quadratic differentials:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Wiley
1987
|
| Schriftenreihe: | Pure and applied mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVII, 236 S. |
| ISBN: | 0471845396 |
Internformat
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| 100 | 1 | |a Gardiner, Frederick P. |d 1939- |e Verfasser |0 (DE-588)140849785 |4 aut | |
| 245 | 1 | 0 | |a Teichmüller theory and quadratic differentials |c Frederick P. Gardiner |
| 264 | 1 | |a New York [u.a.] |b Wiley |c 1987 | |
| 300 | |a XVII, 236 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Pure and applied mathematics | |
| 650 | 4 | |a Applications quasi conformes | |
| 650 | 7 | |a Conforme afbeelding |2 gtt | |
| 650 | 4 | |a Différentielles quadratiques | |
| 650 | 7 | |a Kwadratische differentialen |2 gtt | |
| 650 | 4 | |a Riemann, Surfaces de | |
| 650 | 7 | |a Riemann-vlakken |2 gtt | |
| 650 | 4 | |a Teichmüller, Espaces de | |
| 650 | 7 | |a Teichmüller-ruimten |2 gtt | |
| 650 | 4 | |a Quadratic differentials | |
| 650 | 4 | |a Quasiconformal mappings | |
| 650 | 4 | |a Riemann surfaces | |
| 650 | 4 | |a Teichmüller spaces | |
| 650 | 0 | 7 | |a Riemannsche Fläche |0 (DE-588)4049991-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Teichmüller-Raum |0 (DE-588)4131425-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Quasikonforme Abbildung |0 (DE-588)4199279-9 |2 gnd |9 rswk-swf |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-000457055 | ||
Datensatz im Suchindex
| _version_ | 1804115181878378496 |
|---|---|
| adam_text | CONTENTS
1. Results from Riemann Surface Theory and Quasiconformal
Mapping 1
1.1. Definition of a Riemann Surface, 2
1.2. The Uniformization Theorem, 3
1.3. Metrics of Constant Curvature, 4
1.4. Fuchsian Groups, 7
1.5. Classification of Elements of PSL(2, R), 14
1.6. Fundamental Domains for Fuchsian Groups, 15
1.7. Quasiconformal Mappings: Geometric and Analytic
Definitions, 18
1.8. The Beltrami Equation, 19
1.9. Extremal Length, 21
1.10. Grotzsch s Problem for an Annulus, 26
1.11. The Dimension of the Space of Quadratic Differentials, 27
2. Minimal Norm Properties for Holomorphic Quadratic
Differentials 33
2.1. Trajectories of Quadratic Differentials, 34
2.2. Invariants for Quadratic Differentials, 36
2.3. The First Minimal Norm Property, 37
2.4. The Reich-Strebel Inequality, 41
2.5. Trajectory Structure, 46
2.6. The Second Minimal Norm Property, 54
3. The Reich-Strebel Inequality for Fuchsian Groups 61
3.1. Integrable Cusp Forms, 62
3.2. Trivial Mappings for Fuchsian Groups of the First Kind, 64
3.3. The Reich-Strebel Inequality for Finitely Generated Fuchsian
Groups of the First Kind, 66
XV
xvi CONTENTS
3.4. Trivial Mappings for Groups of the Second Kind, 67
3.5. Finitely Generated Groups of the Second Kind, 68
4. Density Theorems for Quadratic Differentials 71
4.1. Bers s Approximation Theorem, 71
4.2. A Density Theorem for Fuchsian Groups, 78
4.3. Poincare Theta Series, 80
4.4. Kernel Functions for Plane Domains, 80
4.5. The Inequality of Reich and Strebel for Arbitrary Fuchsian
Groups, 85
5. Teichmiiller Theory 91
5.1. Teichmiiller Space on a Riemann Surface, 92
5.2. Teichmuller Space of a Fuchsian Group, 94
5.3. Teichmuller s Metric, 97
5.4. The Bers Embedding of Teichmuller Space, 97
5.5. Translation Mappings between Teichmiiller Spaces, 102
5.6. The Manifold Structure of Teichmuller Space, 103
5.7. The Infinitesimal Theory, 105
5.8. Infinitesimally Trivial Beltrami Differentials, 106
5.9. Teichmuller Spaces of Fuchsian Groups with Boundary, 108
6. Teichmuller s Theorem 117
6.1. The Hamilton-Krushkal Condition: Necessity, 117
6.2. Teichmuller s Theorem: Existence, 119
6.3. Teichmuller s Theorem: Uniqueness, 120
6.4. Inequalities for Functionals of Beltrami Coefficients, 121
6.5. The Hamilton-Krushkal Condition: Sufficiency, 123
6.6. Variation of the Extremal Value, 125
6.7. Finite Dimensional Teichmuller Spaces are
Cells, 125
6.8. Strebel s Frame Mapping Condition, 126
7. Teichmuller s and Kobayashi s Metrics 133
7.1. The Infinitesimal Metric on the Tangent Bundle to T(T, C), 134
7.2. Integration of the Infinitesimal Metric, 137
7.3. The Kobayashi Metric, 138
7.4. The Finite Dimensional Case, 139
7.5. The Infinite Dimensional Case, 144
Appendix: A Lemma of Ahlfors, 146
8. Discontinuity of the Modular Group 149
8.1. Definition of the Modular Group of a Surface, 149
8.2. The Action of the Modular Group on Teichmuller Space, 150
CONTENTS xvii
8.3. Moduli Sets, 153
8.4. The Length Spectrum, 156
8.5. The Discontinuity of the Modular Group, 158
8.6. Automorphism Groups, 160
9. Holomorphic Self-Mappings of Teichmiiller Space 165
9.1. Signature and Type of Fuchsian Groups: A Theorem of Bers and
Greenberg, 166
9.2. Royden s Theorem on Isometries, 169
9.3. The Smoothness of Teichmuller s Metric, 169
9.4. The Nonsmoothness of Teichmuller s Metric, 177
9.5. Weierstrass Points, 180
9.6. Isometries of T(r), 184
10. Quadratic Differentials with Closed Trajectories 191
10.1. Admissible Systems, 192
10.2. An Extremal Problem for Admissible Systems, 193
10.3. Weyl s Lemma, 195
10.4. Existence of Jenkins-Strebel Differentials with Prescribed
Heights, 196
10.5. Uniqueness of Jenkins-Strebel Differentials, 199
11. Measured Foliations 203
11.1. Definition of a Measured Foliation, 205
11.2. Injectivity of the Heights Mapping, 207
11.3. Continuity of the Heights Mapping, 208
11.4. Convergence of Heights Implies Convergence of Quadratic
Differentials, 209
11.5. Intersection Numbers, 210
11.6. Projectivizations, 214
11.7. The Heights Mapping Between Quadratic Differentials on Different
Riemann Surfaces in the Same Teichmiiller Space, 215
11.8. Variation in the Dirichlet Norm, 217
Bibliography 225
Index 233
|
| any_adam_object | 1 |
| author | Gardiner, Frederick P. 1939- |
| author_GND | (DE-588)140849785 |
| author_facet | Gardiner, Frederick P. 1939- |
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| ctrlnum | (OCoLC)15429532 (DE-599)BVBBV000730476 |
| dewey-full | 515/.223 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.223 |
| dewey-search | 515/.223 |
| dewey-sort | 3515 3223 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV000730476 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:18:32Z |
| institution | BVB |
| isbn | 0471845396 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000457055 |
| oclc_num | 15429532 |
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| physical | XVII, 236 S. |
| publishDate | 1987 |
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| spelling | Gardiner, Frederick P. 1939- Verfasser (DE-588)140849785 aut Teichmüller theory and quadratic differentials Frederick P. Gardiner New York [u.a.] Wiley 1987 XVII, 236 S. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics Applications quasi conformes Conforme afbeelding gtt Différentielles quadratiques Kwadratische differentialen gtt Riemann, Surfaces de Riemann-vlakken gtt Teichmüller, Espaces de Teichmüller-ruimten gtt Quadratic differentials Quasiconformal mappings Riemann surfaces Teichmüller spaces Riemannsche Fläche (DE-588)4049991-1 gnd rswk-swf Teichmüller-Raum (DE-588)4131425-6 gnd rswk-swf Quasikonforme Abbildung (DE-588)4199279-9 gnd rswk-swf Teichmüller-Raum (DE-588)4131425-6 s Quasikonforme Abbildung (DE-588)4199279-9 s DE-604 Riemannsche Fläche (DE-588)4049991-1 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000457055&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gardiner, Frederick P. 1939- Teichmüller theory and quadratic differentials Applications quasi conformes Conforme afbeelding gtt Différentielles quadratiques Kwadratische differentialen gtt Riemann, Surfaces de Riemann-vlakken gtt Teichmüller, Espaces de Teichmüller-ruimten gtt Quadratic differentials Quasiconformal mappings Riemann surfaces Teichmüller spaces Riemannsche Fläche (DE-588)4049991-1 gnd Teichmüller-Raum (DE-588)4131425-6 gnd Quasikonforme Abbildung (DE-588)4199279-9 gnd |
| subject_GND | (DE-588)4049991-1 (DE-588)4131425-6 (DE-588)4199279-9 |
| title | Teichmüller theory and quadratic differentials |
| title_auth | Teichmüller theory and quadratic differentials |
| title_exact_search | Teichmüller theory and quadratic differentials |
| title_full | Teichmüller theory and quadratic differentials Frederick P. Gardiner |
| title_fullStr | Teichmüller theory and quadratic differentials Frederick P. Gardiner |
| title_full_unstemmed | Teichmüller theory and quadratic differentials Frederick P. Gardiner |
| title_short | Teichmüller theory and quadratic differentials |
| title_sort | teichmuller theory and quadratic differentials |
| topic | Applications quasi conformes Conforme afbeelding gtt Différentielles quadratiques Kwadratische differentialen gtt Riemann, Surfaces de Riemann-vlakken gtt Teichmüller, Espaces de Teichmüller-ruimten gtt Quadratic differentials Quasiconformal mappings Riemann surfaces Teichmüller spaces Riemannsche Fläche (DE-588)4049991-1 gnd Teichmüller-Raum (DE-588)4131425-6 gnd Quasikonforme Abbildung (DE-588)4199279-9 gnd |
| topic_facet | Applications quasi conformes Conforme afbeelding Différentielles quadratiques Kwadratische differentialen Riemann, Surfaces de Riemann-vlakken Teichmüller, Espaces de Teichmüller-ruimten Quadratic differentials Quasiconformal mappings Riemann surfaces Teichmüller spaces Riemannsche Fläche Teichmüller-Raum Quasikonforme Abbildung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000457055&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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