Weil-Petersson metric on the universal Teichmüller space:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
2006
|
| Schriftenreihe: | Memoirs of the American Mathematical Society
861 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VII, 119 S. |
| ISBN: | 9780821839362 0821839365 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV021743763 | ||
| 003 | DE-604 | ||
| 005 | 20150326 | ||
| 007 | t | ||
| 008 | 060926s2006 |||| 00||| eng d | ||
| 020 | |a 9780821839362 |9 978-0-8218-3936-2 | ||
| 020 | |a 0821839365 |9 0-8218-3936-5 | ||
| 035 | |a (OCoLC)473730224 | ||
| 035 | |a (DE-599)BVBBV021743763 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-355 |a DE-29T |a DE-11 |a DE-188 |a DE-83 | ||
| 084 | |a 58B25 |2 msc | ||
| 084 | |a 58B20 |2 msc | ||
| 084 | |a 30C55 |2 msc | ||
| 084 | |a 30F60 |2 msc | ||
| 084 | |a 32G15 |2 msc | ||
| 084 | |a 46E20 |2 msc | ||
| 100 | 1 | |a Takhtajan, Leon A. |d 1950- |e Verfasser |0 (DE-588)123335868 |4 aut | |
| 245 | 1 | 0 | |a Weil-Petersson metric on the universal Teichmüller space |c Leon A. Takhtajan ; Lee-Peng Teo |
| 246 | 1 | 3 | |a Weil Petersson metric on the universal Teichmüller space |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 2006 | |
| 300 | |a VII, 119 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society |v 861 | |
| 650 | 0 | 7 | |a Schlichte Funktion |0 (DE-588)4131418-9 |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 Riemannsche Fläche |0 (DE-588)4049991-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Teichmüller-Raum |0 (DE-588)4131425-6 |D s |
| 689 | 0 | 1 | |a Schlichte Funktion |0 (DE-588)4131418-9 |D s |
| 689 | 0 | 2 | |a Riemannsche Fläche |0 (DE-588)4049991-1 |D s |
| 689 | 0 | |C b |5 DE-604 | |
| 700 | 1 | |a Teo, Lee-Peng |d 1975- |e Verfasser |0 (DE-588)173860176 |4 aut | |
| 830 | 0 | |a Memoirs of the American Mathematical Society |v 861 |w (DE-604)BV008000141 |9 861 | |
| 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=014957075&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-014957075 | ||
Datensatz im Suchindex
| _version_ | 1804135596985155584 |
|---|---|
| adam_text | Contents
Introduction 1
Chapter 1. Curvature Properties and Chern Forms 7
1. The universal Teiehniiiller space 7
1.1. Teiehniiiller theory 7
1.1.1. Main definitions 7
1.1.2. The group structure 8
1.1.3. The Bers embedding 9
1.1.4. The complex structure 10
1.1.5. The universal Teiehniiiller curve 10
1.2. Homogeneous space* of Homeo(/.S(S1) 11
1.2.1. Confornial welding 11
1.2.2. The horizontal and vertical subspaces 11
1.2.3. The isomorphisms of the tangent spaces 15
1.3. Teiehniiiller spaces and Teiehniiiller curves of Fuchsian groups 17
1.4. Resolvent kernel 18
1.5. Variational formulas 19
2. T(l) as a Hilbert manifold 22
2.1. Hilbert space structure on tangent spaces 22
2.2. The L2-estimates 27
2.3. The Hilbert manifold structure of T(l) 29
2.4. Integral manifolds of the distribution T)t 31
3. 7o(l) as a topological group 32
4. Velling-Kirillov and Weil-Pet ersson metrics 36
4.1. Velling-Kirillov metric on the universal Teichmiiller curve 30
4.2. Weil-Pet ersson metric on the universal Teichmiiller space 37
5. Characteristic forms of the universal Teichmiiller curve 38
5.1. The form c {V) as Velling-Kirillov symplectic form 39
5.2. The Chern form c (V) and the resolvent kernel 41
5.3. Mumford-Morita-Miller characteristic forms 43
6. First and second variations of the hyperbolic metric 44
6.1. The first variation 44
6.2. The second variation 44
7. Riemann curvature tensor 46
7.1. The first variation of the Weil-Pet ersson metric 46
7.2. The second variation of the Weil-Pet ersson metric 50
7.3. Ricci and sectional curvatures 54
8. Finite-dimensional Teichmiiller spaces 56
Chapter 2. Kahler Potential and Period Mapping 65
V
vi CONTENTS
1. Hilbert spaces and univalent functions 65
2. Grunsky operators for T0(l) 70
2.1. Grunsky coefficients and operators 70
2.2. Fredholm eigenvalues and Predholm determinant 78
2.3. Period matrix of 1-forms 82
3. Variations of the functions Si and S2 83
3.1. The first variation of S2 84
3.2. The first variation of Si 85
4. Weil-Petersson potential 95
4.1. Weil-Petersson potential on T0(l) 95
4.2. Weil-Petersson potential on T(l) 97
5. The period mapping 97
5.1. KYNS period mapping 98
5.2. Embeddings into the Segal-Wilson universal Grassmannian 101
Appendix A. The Hilbert Manifold Structure of T0(l) 105
Appendix B. The Period Mapping 109
Bibliography 117
|
| adam_txt |
Contents
Introduction 1
Chapter 1. Curvature Properties and Chern Forms 7
1. The universal Teiehniiiller space 7
1.1. Teiehniiiller theory 7
1.1.1. Main definitions 7
1.1.2. The group structure 8
1.1.3. The Bers embedding 9
1.1.4. The complex structure 10
1.1.5. The universal Teiehniiiller curve 10
1.2. Homogeneous space* of Homeo(/.S(S1) 11
1.2.1. Confornial welding 11
1.2.2. The horizontal and vertical subspaces 11
1.2.3. The isomorphisms of the tangent spaces 15
1.3. Teiehniiiller spaces and Teiehniiiller curves of Fuchsian groups 17
1.4. Resolvent kernel 18
1.5. Variational formulas 19
2. T(l) as a Hilbert manifold 22
2.1. Hilbert space structure on tangent spaces 22
2.2. The L2-estimates 27
2.3. The Hilbert manifold structure of T(l) 29
2.4. Integral manifolds of the distribution T)t 31
3. 7o(l) as a topological group 32
4. Velling-Kirillov and Weil-Pet ersson metrics 36
4.1. Velling-Kirillov metric on the universal Teichmiiller curve 30
4.2. Weil-Pet ersson metric on the universal Teichmiiller space 37
5. Characteristic forms of the universal Teichmiiller curve 38
5.1. The form c\{V) as Velling-Kirillov symplectic form 39
5.2. The Chern form c\(V) and the resolvent kernel 41
5.3. Mumford-Morita-Miller characteristic forms 43
6. First and second variations of the hyperbolic metric 44
6.1. The first variation 44
6.2. The second variation 44
7. Riemann curvature tensor 46
7.1. The first variation of the Weil-Pet ersson metric 46
7.2. The second variation of the Weil-Pet ersson metric 50
7.3. Ricci and sectional curvatures 54
8. Finite-dimensional Teichmiiller spaces 56
Chapter 2. Kahler Potential and Period Mapping 65
V
vi CONTENTS
1. Hilbert spaces and univalent functions 65
2. Grunsky operators for T0(l) 70
2.1. Grunsky coefficients and operators 70
2.2. Fredholm eigenvalues and Predholm determinant 78
2.3. Period matrix of 1-forms 82
3. Variations of the functions Si and S2 83
3.1. The first variation of S2 84
3.2. The first variation of Si 85
4. Weil-Petersson potential 95
4.1. Weil-Petersson potential on T0(l) 95
4.2. Weil-Petersson potential on T(l) 97
5. The period mapping 97
5.1. KYNS period mapping 98
5.2. Embeddings into the Segal-Wilson universal Grassmannian 101
Appendix A. The Hilbert Manifold Structure of T0(l) 105
Appendix B. The Period Mapping 109
Bibliography 117 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Takhtajan, Leon A. 1950- Teo, Lee-Peng 1975- |
| author_GND | (DE-588)123335868 (DE-588)173860176 |
| author_facet | Takhtajan, Leon A. 1950- Teo, Lee-Peng 1975- |
| author_role | aut aut |
| author_sort | Takhtajan, Leon A. 1950- |
| author_variant | l a t la lat l p t lpt |
| building | Verbundindex |
| bvnumber | BV021743763 |
| ctrlnum | (OCoLC)473730224 (DE-599)BVBBV021743763 |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01966nam a2200481 cb4500</leader><controlfield tag="001">BV021743763</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20150326 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">060926s2006 |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780821839362</subfield><subfield code="9">978-0-8218-3936-2</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0821839365</subfield><subfield code="9">0-8218-3936-5</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)473730224</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV021743763</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-355</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-83</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">58B25</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">58B20</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">30C55</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">30F60</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">32G15</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">46E20</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Takhtajan, Leon A.</subfield><subfield code="d">1950-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)123335868</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Weil-Petersson metric on the universal Teichmüller space</subfield><subfield code="c">Leon A. Takhtajan ; Lee-Peng Teo</subfield></datafield><datafield tag="246" ind1="1" ind2="3"><subfield code="a">Weil Petersson metric on the universal Teichmüller space</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Providence, RI</subfield><subfield code="b">American Math. Soc.</subfield><subfield code="c">2006</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">VII, 119 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Memoirs of the American Mathematical Society</subfield><subfield code="v">861</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Schlichte Funktion</subfield><subfield code="0">(DE-588)4131418-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Teichmüller-Raum</subfield><subfield code="0">(DE-588)4131425-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Riemannsche Fläche</subfield><subfield code="0">(DE-588)4049991-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Teichmüller-Raum</subfield><subfield code="0">(DE-588)4131425-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Schlichte Funktion</subfield><subfield code="0">(DE-588)4131418-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Riemannsche Fläche</subfield><subfield code="0">(DE-588)4049991-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="C">b</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Teo, Lee-Peng</subfield><subfield code="d">1975-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)173860176</subfield><subfield code="4">aut</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Memoirs of the American Mathematical Society</subfield><subfield code="v">861</subfield><subfield code="w">(DE-604)BV008000141</subfield><subfield code="9">861</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014957075&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-014957075</subfield></datafield></record></collection> |
| id | DE-604.BV021743763 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T15:30:06Z |
| indexdate | 2024-07-09T20:43:02Z |
| institution | BVB |
| isbn | 9780821839362 0821839365 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014957075 |
| oclc_num | 473730224 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-29T DE-11 DE-188 DE-83 |
| owner_facet | DE-355 DE-BY-UBR DE-29T DE-11 DE-188 DE-83 |
| physical | VII, 119 S. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Takhtajan, Leon A. 1950- Verfasser (DE-588)123335868 aut Weil-Petersson metric on the universal Teichmüller space Leon A. Takhtajan ; Lee-Peng Teo Weil Petersson metric on the universal Teichmüller space Providence, RI American Math. Soc. 2006 VII, 119 S. txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society 861 Schlichte Funktion (DE-588)4131418-9 gnd rswk-swf Teichmüller-Raum (DE-588)4131425-6 gnd rswk-swf Riemannsche Fläche (DE-588)4049991-1 gnd rswk-swf Teichmüller-Raum (DE-588)4131425-6 s Schlichte Funktion (DE-588)4131418-9 s Riemannsche Fläche (DE-588)4049991-1 s b DE-604 Teo, Lee-Peng 1975- Verfasser (DE-588)173860176 aut Memoirs of the American Mathematical Society 861 (DE-604)BV008000141 861 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014957075&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Takhtajan, Leon A. 1950- Teo, Lee-Peng 1975- Weil-Petersson metric on the universal Teichmüller space Memoirs of the American Mathematical Society Schlichte Funktion (DE-588)4131418-9 gnd Teichmüller-Raum (DE-588)4131425-6 gnd Riemannsche Fläche (DE-588)4049991-1 gnd |
| subject_GND | (DE-588)4131418-9 (DE-588)4131425-6 (DE-588)4049991-1 |
| title | Weil-Petersson metric on the universal Teichmüller space |
| title_alt | Weil Petersson metric on the universal Teichmüller space |
| title_auth | Weil-Petersson metric on the universal Teichmüller space |
| title_exact_search | Weil-Petersson metric on the universal Teichmüller space |
| title_exact_search_txtP | Weil-Petersson metric on the universal Teichmüller space |
| title_full | Weil-Petersson metric on the universal Teichmüller space Leon A. Takhtajan ; Lee-Peng Teo |
| title_fullStr | Weil-Petersson metric on the universal Teichmüller space Leon A. Takhtajan ; Lee-Peng Teo |
| title_full_unstemmed | Weil-Petersson metric on the universal Teichmüller space Leon A. Takhtajan ; Lee-Peng Teo |
| title_short | Weil-Petersson metric on the universal Teichmüller space |
| title_sort | weil petersson metric on the universal teichmuller space |
| topic | Schlichte Funktion (DE-588)4131418-9 gnd Teichmüller-Raum (DE-588)4131425-6 gnd Riemannsche Fläche (DE-588)4049991-1 gnd |
| topic_facet | Schlichte Funktion Teichmüller-Raum Riemannsche Fläche |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014957075&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
| work_keys_str_mv | AT takhtajanleona weilpeterssonmetricontheuniversalteichmullerspace AT teoleepeng weilpeterssonmetricontheuniversalteichmullerspace |