Quasiconformal maps and Teichmüller theory:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford
Oxford University Press
2007
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Oxford graduate texts in mathematics
11 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | VIII, 189 S. graph. Darst. |
| ISBN: | 9780198569268 0198569262 |
Internformat
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| 100 | 1 | |a Fletcher, Alastair |4 aut | |
| 245 | 1 | 0 | |a Quasiconformal maps and Teichmüller theory |c A. Fletcher and V. Markovic |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Oxford |b Oxford University Press |c 2007 | |
| 300 | |a VIII, 189 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Oxford graduate texts in mathematics |v 11 | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 4 | |a Quasiconformal mappings | |
| 650 | 4 | |a Teichmüller spaces | |
| 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 |
| 689 | 0 | 0 | |a Quasikonforme Abbildung |0 (DE-588)4199279-9 |D s |
| 689 | 0 | 1 | |a Teichmüller-Raum |0 (DE-588)4131425-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Marković, Vladimir |4 aut | |
| 830 | 0 | |a Oxford graduate texts in mathematics |v 11 |w (DE-604)BV011416591 |9 11 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015054064&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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Datensatz im Suchindex
| _version_ | 1804135777122123776 |
|---|---|
| adam_text | Contents
1 The Grotzsch argument 1
1.1 Maps on rectangles 1
1.2 Some definitions 2
1.3 Solving the Grotzsch problem 3
1.4 Composed mappings 5
1.5 Riemann surfaces 7
2 Geometric definition of quasiconformal maps 10
2.1 Extremal length 11
2.2 Curve families 13
2.3 Geometric definition of quasiconformal maps 14
3 Analytic properties of quasiconformal maps 19
3.1 Analytic definition and corollaries 19
3.2 Extremal ring domains 23
3.3 Holder continuity 26
3.4 Compactness properties of quasiconformal maps 29
4 Quasi-isometries and quasisymmetric maps 31
4.1 Cross-ratio 31
4.2 Quasisymmetric maps 32
4.3 Quasi-isometry 36
4.4 The barycentric extension 41
5 The Beltrami differential equation 48
5.1 Integral transforms 48
5.2 Solution of the Beltrami equation 51
5.3 Dependence on Beltrami coefficients 57
6 Holomorphic motions and applications 64
6.1 Holomorphic motions 64
6.2 Equivariant extensions 68
6.3 Area distortion 71
viii Contents
7 Teichmiiller spaces 76
7.1 Universal Teichmiiller space 76
7.2 Teichmuller space of a Riemann surface 77
7.3 Teichmiiller metric 80
7.4 The Teichmuller space of a torus 84
7.5 Schwarzian derivatives and quadratic differentials 88
7.6 The Bers embedding 92
7.7 Complex structure on Teichmuller space 97
8 Extremal quasiconformal mappings 104
8.1 Examples of extremal mappings 104
8.2 The Hamilton-Krushkal condition 109
8.3 The Main Inequality 116
8.4 Sufficiency of the Hamilton-Krushkal condition 118
9 Unique extremality 123
9.1 The frame mapping condition 123
9.2 Some necessary conditions for unique extremality 130
9.3 Delta inequalities 132
9.4 Beltrami differentials with constant modulus 135
9.5 Beltrami differentials with non-constant modulus 139
9.6 Hahn-Banach extensions 145
10 Isomorphisms of Teichmuller space 149
10.1 The Kobayashi metric 149
10.2 Equimeasurability 152
10.3 Isometries of Bergman spaces 156
10.4 Geometric isometries in the general case 159
10.5 Biholomorphic maps between Teichmuller spaces 171
11 Local rigidity of Teichmuller spaces 173
11.1 Bergman kernels 173
11.2 Operators on AX(M) 177
11.3 An isomorphism between A1 (M) and I1 180
11.4 Local bi-Lipschitz equivalence of Teichmuller spaces 182
References 184
Index 188
|
| adam_txt |
Contents
1 The Grotzsch argument 1
1.1 Maps on rectangles 1
1.2 Some definitions 2
1.3 Solving the Grotzsch problem 3
1.4 Composed mappings 5
1.5 Riemann surfaces 7
2 Geometric definition of quasiconformal maps 10
2.1 Extremal length 11
2.2 Curve families 13
2.3 Geometric definition of quasiconformal maps 14
3 Analytic properties of quasiconformal maps 19
3.1 Analytic definition and corollaries 19
3.2 Extremal ring domains 23
3.3 Holder continuity 26
3.4 Compactness properties of quasiconformal maps 29
4 Quasi-isometries and quasisymmetric maps 31
4.1 Cross-ratio 31
4.2 Quasisymmetric maps 32
4.3 Quasi-isometry 36
4.4 The barycentric extension 41
5 The Beltrami differential equation 48
5.1 Integral transforms 48
5.2 Solution of the Beltrami equation 51
5.3 Dependence on Beltrami coefficients 57
6 Holomorphic motions and applications 64
6.1 Holomorphic motions 64
6.2 Equivariant extensions 68
6.3 Area distortion 71
viii Contents
7 Teichmiiller spaces 76
7.1 Universal Teichmiiller space 76
7.2 Teichmuller space of a Riemann surface 77
7.3 Teichmiiller metric 80
7.4 The Teichmuller space of a torus 84
7.5 Schwarzian derivatives and quadratic differentials 88
7.6 The Bers embedding 92
7.7 Complex structure on Teichmuller space 97
8 Extremal quasiconformal mappings 104
8.1 Examples of extremal mappings 104
8.2 The Hamilton-Krushkal condition 109
8.3 The Main Inequality 116
8.4 Sufficiency of the Hamilton-Krushkal condition 118
9 Unique extremality 123
9.1 The frame mapping condition 123
9.2 Some necessary conditions for unique extremality 130
9.3 Delta inequalities 132
9.4 Beltrami differentials with constant modulus 135
9.5 Beltrami differentials with non-constant modulus 139
9.6 Hahn-Banach extensions 145
10 Isomorphisms of Teichmuller space 149
10.1 The Kobayashi metric 149
10.2 Equimeasurability 152
10.3 Isometries of Bergman spaces 156
10.4 Geometric isometries in the general case 159
10.5 Biholomorphic maps between Teichmuller spaces 171
11 Local rigidity of Teichmuller spaces 173
11.1 Bergman kernels 173
11.2 Operators on AX(M) 177
11.3 An isomorphism between A1 (M) and I1 180
11.4 Local bi-Lipschitz equivalence of Teichmuller spaces 182
References 184
Index 188 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Fletcher, Alastair Marković, Vladimir |
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| dewey-full | 515.94 |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 1. publ. |
| format | Book |
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| illustrated | Illustrated |
| index_date | 2024-07-02T16:00:46Z |
| indexdate | 2024-07-09T20:45:53Z |
| institution | BVB |
| isbn | 9780198569268 0198569262 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015054064 |
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| physical | VIII, 189 S. graph. Darst. |
| publishDate | 2007 |
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| publisher | Oxford University Press |
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| series | Oxford graduate texts in mathematics |
| series2 | Oxford graduate texts in mathematics |
| spelling | Fletcher, Alastair aut Quasiconformal maps and Teichmüller theory A. Fletcher and V. Markovic 1. publ. Oxford Oxford University Press 2007 VIII, 189 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford graduate texts in mathematics 11 Hier auch später erschienene, unveränderte Nachdrucke Quasiconformal mappings Teichmüller spaces Teichmüller-Raum (DE-588)4131425-6 gnd rswk-swf Quasikonforme Abbildung (DE-588)4199279-9 gnd rswk-swf Quasikonforme Abbildung (DE-588)4199279-9 s Teichmüller-Raum (DE-588)4131425-6 s DE-604 Marković, Vladimir aut Oxford graduate texts in mathematics 11 (DE-604)BV011416591 11 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015054064&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fletcher, Alastair Marković, Vladimir Quasiconformal maps and Teichmüller theory Oxford graduate texts in mathematics Quasiconformal mappings Teichmüller spaces Teichmüller-Raum (DE-588)4131425-6 gnd Quasikonforme Abbildung (DE-588)4199279-9 gnd |
| subject_GND | (DE-588)4131425-6 (DE-588)4199279-9 |
| title | Quasiconformal maps and Teichmüller theory |
| title_auth | Quasiconformal maps and Teichmüller theory |
| title_exact_search | Quasiconformal maps and Teichmüller theory |
| title_exact_search_txtP | Quasiconformal maps and Teichmüller theory |
| title_full | Quasiconformal maps and Teichmüller theory A. Fletcher and V. Markovic |
| title_fullStr | Quasiconformal maps and Teichmüller theory A. Fletcher and V. Markovic |
| title_full_unstemmed | Quasiconformal maps and Teichmüller theory A. Fletcher and V. Markovic |
| title_short | Quasiconformal maps and Teichmüller theory |
| title_sort | quasiconformal maps and teichmuller theory |
| topic | Quasiconformal mappings Teichmüller spaces Teichmüller-Raum (DE-588)4131425-6 gnd Quasikonforme Abbildung (DE-588)4199279-9 gnd |
| topic_facet | Quasiconformal mappings Teichmüller spaces Teichmüller-Raum Quasikonforme Abbildung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015054064&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011416591 |
| work_keys_str_mv | AT fletcheralastair quasiconformalmapsandteichmullertheory AT markovicvladimir quasiconformalmapsandteichmullertheory |