Quasiconformal Teichmüller theory:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[2000]
|
| Series: | Mathematical surveys and monographs
Volume 76 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xix, 372 Seiten |
| ISBN: | 0821819836 9780821819838 |
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MARC
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| 100 | 1 | |a Gardiner, Frederick P. |d 1939- |e Verfasser |0 (DE-588)140849785 |4 aut | |
| 245 | 1 | 0 | |a Quasiconformal Teichmüller theory |c Frederick P. Gardiner ; Nikola Lakic |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2000] | |
| 264 | 4 | |c © 2000 | |
| 300 | |a xix, 372 Seiten | ||
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| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematical surveys and monographs |v Volume 76 | |
| 650 | 4 | |a Teichmüller-Raum - Quasikonforme Abbildung | |
| 650 | 0 | 7 | |a Teichmüller-Raum |0 (DE-588)4131425-6 |2 gnd |9 rswk-swf |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
PREFACE xiii
ACKNOWLEDGEMENTS xix
1. QUASICONFORMAL MAPPING 1
1.1 From Conformal to Quasiconformal 1
1.2 Linear Quasiconformality 2
1.3 Analytic Quasiconformality 4
1.4 Geometric Quasiconformality 7
1.5 Solving the Beltrami Equation 10
1.6 Holomorphic Motions 12
1.7 Lebesgue Measure and Hausdorff Dimension 13
2. RIEMANN SURFACES 17
2.1 Conformal Structure 18
2.2 Examples and Uniformization 18
2.3 Extremal Length 21
2.4 Teichmiiller Space 24
2.5 Metrics of Constant Curvature 26
2.6 Thrice-Punctured Spheres 30
2.7 Fuchsian Groups 31
2.8 Types of Elements of PSL(2, R) 37
2.9 Fundamental Domains 38
2.10 Dimension of Quadratic Differentials 41
3. QUADRATIC DIFFERENTIALS, PART I 43
3.1 Integrable Quadratic Differentials 46
3.2 Poincare Theta Series 49
3.3 Predual Space 52
3.4 Closed Sets 54
3.5 The Teichmiiller Infinitesimal Norm 58
3.6 Cross-Ratio Norm on Z(A) 59
3.7 Approximation by Rational Functions 62
3.8 Rational Quadratic Differentials 66
3.9 The Equivalence Theorem 67
vii
viii CONTENTS
3.10 Vanishing Elements of Z(A) 70
Appendix, Proof of the Equivalence Theorem 73
4. QUADRATIC DIFFERENTIALS, PART II 83
4.1 Horizontal Trajectories 84
4.2 Geodesic Trajectories 86
4.3 The Minimal Norm Property 89
4.4 The Reich-Strebel Inequality 93
4.5 Surfaces of Infinite Analytic Type 94
4.6 The Main Inequality and Uniqueness 95
4.7 The Frame Mapping Theorem 96
4.8 Infinitesimal Frame Mapping 99
4.9 The Fundamental Inequalities 101
4.10 Teichmuller Contraction 102
4.11 Strebel Points 104
4.12 Teichmiiller s Infinitesimal Metric 106
5. TEICHMULLER EQUIVALENCE 109
5.1 Conformally Natural Extension 109
5.2 Quasiconformal Isotopies 116
5.3 Isotopies over Plane Domains 119
5.4 Proof of Lemma 2 121
6. THE BERS EMBEDDING 125
6.1 Cross-Ratios and Schwarzian Derivatives 126
6.2 Schwarzian Distortion 131
6.3 The Bers Embedding 132
6.4 The Manifold Structure 135
6.5 The Infinitesimal Theory 138
6.6 Infmitesimally Trivial Beltrami Differentials 140
6.7 Hamilton-Krushkal Necessary Condition 141
7. KOBAYASHI S METRIC ON TEICHMULLER SPACE 145
7.1 Kobayashi s Metric 145
7.2 Teichmiiller s and Kobayashi s Metrics 147
7.3 The Lifting Theorem 149
7.4 Uniqueness of Geodesies 151
8. ISOMORPHISMS AND AUTOMORPHISMS 155
8.1 Global to Local 155
8.2 Automorphisms of Teichmuller Discs 157
8.3 Rotational Transitivity 159
8.4 Adjointness Theorem 161
8.5 Isometries of Teichmuller Spaces 162
8.6 The Isometry Property 163
CONTENTS ix
8.7 Nonsmoothness of the Norm 164
8.8 Isometry Theorem for Genus Zero 166
8.9 Riemann Surfaces of Finite Genus 170
9. TEICHMULLER UNIQUENESS 177
9.1 Infinitesimal Main Inequality 178
9.2 Constant Absolute Value 179
9.3 Teichmuller Differentials 183
9.4 Delta Inequalities 186
9.5 Infinitesimal Teichmuller Uniqueness 189
9.6 Unique Holomorphic Motions 191
10. THE MAPPING CLASS GROUP 195
10.1 MCG for the Covering Group 196
10.2 Moduli Sets 196
10.3 The Length Spectrum 199
10.4 Discreteness of Orbits 201
10.5 Automorphism Groups 203
11. JENKINS-STREBEL DIFFERENTIALS 207
11.1 Admissible Systems 208
11.2 An Extremal Problem 209
11.3 Weyl s Lemma 211
11.4 Prescribing Heights 212
11.5 Uniqueness 214
11.6 Examples 215
11.7 Differentials with Two Directions 219
12. MEASURED FOLIATIONS 223
12.1 Definition of a Measured Foliation 225
12.2 Continuity of the Heights Mapping 228
12.3 Convergence 229
12.4 Intersection Numbers 230
12.5 Projectivizations 233
12.6 The Heights Mapping 234
12.7 Variation of the Dirichlet Norm 236
13. OBSTACLE PROBLEMS 241
13.1 Extremal Problem for the Disc 242
13.2 Extremal Problem for a Surface 244
13.3 Smoothing the Contours 245
13.4 Boundedness of the Norm 245
13.5 Schiffer and Beltrami Variations 248
13.6 Existence 250
13.7 Uniqueness 251
x CONTENTS
13.8 Slit Mappings 253
13.9 Trajectories around the Obstacle 254
14. ASYMPTOTIC TEICHMULLER SPACE 257
14.1 The Infinitesimal Theory 258
14.2 Harmonic Beltrami Differentials 260
14.3 The Earle-Nag Reflection 263
14.4 Generalized Ahlfors-Weill Sections 266
14.5 Bers £-Operators 268
14.6 Inverse Operators 269
14.7 Manifold Structure 271
14.8 Inequalities for Boundary Dilatation 275
14.9 Contraction 276
14.10 Extremality in AT 281
14.11 Teichmiiller s Metric 282
15. ASYMPTOTICALLY EXTREMAL MAPS 285
15.1 Weighted Beltrami Differentials 286
15.2 Asymptotic Beltrami Differentials 288
15.3 Weighted Beltrami Coefficients 290
15.4 Asymptotic Beltrami Coefficients 296
16. UNIVERSAL TEICHMULLER SPACE 299
16.1 Quasisymmetric Homeomorphisms 299
16.2 Partial Topological Groups 301
16.3 Symmetric Homeomorphisms 302
16.4 Beurling-Ahlfors Extension 305
16.5 Welding 307
16.6 Zygmund Spaces 315
16.7 The Hilbert Transform 319
16.8 Global Coordinates for QS mod S 320
17. SUBSTANTIAL BOUNDARY POINTS 323
17.1 Local Dilatation 323
17.2 Unit Disc Case 325
17.3 Boundary Dilatation 327
17.4 Infinitesimally Substantial Points 329
17.5 Local Boundary Seminorms 330
17.6 Local Boundary Dilatation 331
17.7 Asymptotic Hamilton Sequences 333
18. EARTHQUAKE MAPPINGS 337
18.1 Finite Earthquakes 337
18.2 General Earthquakes 343
18.3 Simple Earthquakes and Bends 346
CONTENTS xi
18.4 The Linear Theory 348
18.5 Infinitesimal Earthquakes 350
Bibliography 357
Index 369
|
| any_adam_object | 1 |
| author | Gardiner, Frederick P. 1939- Lakic, Nikola 1966- |
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| id | DE-604.BV013265725 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:42:46Z |
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| isbn | 0821819836 9780821819838 |
| language | English |
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| physical | xix, 372 Seiten |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | American Mathematical Society |
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| series2 | Mathematical surveys and monographs |
| spelling | Gardiner, Frederick P. 1939- Verfasser (DE-588)140849785 aut Quasiconformal Teichmüller theory Frederick P. Gardiner ; Nikola Lakic Providence, Rhode Island American Mathematical Society [2000] © 2000 xix, 372 Seiten txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs Volume 76 Teichmüller-Raum - Quasikonforme Abbildung Teichmüller-Raum (DE-588)4131425-6 gnd rswk-swf Teichmüller-Raum (DE-588)4131425-6 s DE-604 Lakic, Nikola 1966- Verfasser (DE-588)14086749X aut Erscheint auch als Online-Ausgabe 978-1-4704-1303-3 Mathematical surveys and monographs Volume 76 (DE-604)BV000018014 76 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009043613&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gardiner, Frederick P. 1939- Lakic, Nikola 1966- Quasiconformal Teichmüller theory Mathematical surveys and monographs Teichmüller-Raum - Quasikonforme Abbildung Teichmüller-Raum (DE-588)4131425-6 gnd |
| subject_GND | (DE-588)4131425-6 |
| title | Quasiconformal Teichmüller theory |
| title_auth | Quasiconformal Teichmüller theory |
| title_exact_search | Quasiconformal Teichmüller theory |
| title_full | Quasiconformal Teichmüller theory Frederick P. Gardiner ; Nikola Lakic |
| title_fullStr | Quasiconformal Teichmüller theory Frederick P. Gardiner ; Nikola Lakic |
| title_full_unstemmed | Quasiconformal Teichmüller theory Frederick P. Gardiner ; Nikola Lakic |
| title_short | Quasiconformal Teichmüller theory |
| title_sort | quasiconformal teichmuller theory |
| topic | Teichmüller-Raum - Quasikonforme Abbildung Teichmüller-Raum (DE-588)4131425-6 gnd |
| topic_facet | Teichmüller-Raum - Quasikonforme Abbildung Teichmüller-Raum |
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| volume_link | (DE-604)BV000018014 |
| work_keys_str_mv | AT gardinerfrederickp quasiconformalteichmullertheory AT lakicnikola quasiconformalteichmullertheory |