Teichmüller theory in Riemannian geometry: based on lecture notes by Jochen Denzler
Saved in:
| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Basel ; Boston, Mass. ; Berlin
Birkhäuser Verlag
1992
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| Series: | Lectures in Mathematics ETH Zürich
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 220 Seiten graph. Darst. |
| ISBN: | 3764327359 0817627359 |
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| 245 | 1 | 0 | |a Teichmüller theory in Riemannian geometry |b based on lecture notes by Jochen Denzler |c Anthony J. Tromba |
| 264 | 1 | |a Basel ; Boston, Mass. ; Berlin |b Birkhäuser Verlag |c 1992 | |
| 300 | |a 220 Seiten |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 0 | |a Lectures in Mathematics ETH Zürich | |
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Record in the Search Index
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| adam_text | Contents
0 Mathematical Preliminaries G
1 The Manifolds of Teichmiiller Theory
1.1 The Manifolds A and A3 14
1.2 The Riemannian Manifolds M and M 18
1.3 The Diffeomorphism M*/V S As 19
1.4 Some Differential Operators and their Adjoints 26
1.5 Proof of Poincare s Theorem 29
1.6 The Manifold Ms_x and the Diffeomorphism with M /V 33
2 The Construction of Teichmiiller Space
2.1 A Rapid Course in Geodesic Theory 36
2.2 The Free Action of T 0 on M-i 38
2.3 The Proper Action of 2 0 on M -1 41
2.4 The Construction of Teichmiiller Space 44
2.5 The Principal Bundles of Teichnuiller Theory 50
2.6 The Weil-Petersson Metric onJ(M) 60
4 Contents
3 T(M) is a Cell
3.1 Dirichlet s Energy on Teichmuller Space 63
3.2 The Properness of Dirichlet s Energy 74
3.3 Teichmuller Space is a Cell 78
3.4 Topological Implications; The Contractibility of T 0 81
4 The Complex Structure on Teichmuller Space
4.1 Almost Complex Principal Fibre Bundles 83
4.2 Abresch-Fischer Holomorphic Coordinates for A 90
4.3 Abresch-Fischer Holomorphic Coordinates for T(M) 94
5 Properties of the Weil-Petersson Metric
5.1 The Weil-Petersson Metric is Kahler 96
5.2 The Natural Algebraic Connection on A 102
5.3 Further Properties of the Algebraic Connection and the
non-Integrability of the Horizontal Distribution on A 106
5.4 The Curvature of Teichmuller Space with Respect to its
Weil-Petersson Metric Ill
5.5 An Asymptotic Property of Weil-Petersson Geodesies 121
6 The Pluri-Subharmonicity of Dirichlet s Energy on T(M);
T(M) is a Stein-Manifold
6.1 Pluri-Subharmonic Functions and Complex Manifolds 123
6.2 Dirichlet s Energy is Strictly Pluri-Subharmonic 126
6.3 Wolf s Form of Dirichlet s Energy on T(M) is Strictly
Weil-Petersson Convex 138
6.4 The Nielsen Realization Problem 152
Contents 5
A Proof of Lichnerowicz Formula 155
B On Harmonic Maps 158
C The Mumford Compactness Theorem 184
D Proof of the Collar Lemma 192
E The Levi-Form of Dirichlet s Energy 196
F Riemann-Roch and the Dimension of Teichmiiller Space 201
Bibliography 205
Indexes
Index of Notation 214
A Chart of the Maps Used 218
Index of Key Words 219
|
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| ctrlnum | (OCoLC)638786102 (DE-599)BVBBV005399276 |
| discipline | Mathematik |
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| id | DE-604.BV005399276 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:28:58Z |
| institution | BVB |
| isbn | 3764327359 0817627359 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003380571 |
| oclc_num | 638786102 |
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| physical | 220 Seiten graph. Darst. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Birkhäuser Verlag |
| record_format | marc |
| series2 | Lectures in Mathematics ETH Zürich |
| spelling | Tromba, Anthony J. 1943- Verfasser (DE-588)142684996 aut Teichmüller theory in Riemannian geometry based on lecture notes by Jochen Denzler Anthony J. Tromba Basel ; Boston, Mass. ; Berlin Birkhäuser Verlag 1992 220 Seiten graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lectures in Mathematics ETH Zürich Teichmüller, Espacios de Variedades Riemannianas Teichmüller-Raum (DE-588)4131425-6 gnd rswk-swf Riemannsche Geometrie (DE-588)4128462-8 gnd rswk-swf Riemannsche Geometrie (DE-588)4128462-8 s Teichmüller-Raum (DE-588)4131425-6 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003380571&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Tromba, Anthony J. 1943- Teichmüller theory in Riemannian geometry based on lecture notes by Jochen Denzler Teichmüller, Espacios de Variedades Riemannianas Teichmüller-Raum (DE-588)4131425-6 gnd Riemannsche Geometrie (DE-588)4128462-8 gnd |
| subject_GND | (DE-588)4131425-6 (DE-588)4128462-8 |
| title | Teichmüller theory in Riemannian geometry based on lecture notes by Jochen Denzler |
| title_auth | Teichmüller theory in Riemannian geometry based on lecture notes by Jochen Denzler |
| title_exact_search | Teichmüller theory in Riemannian geometry based on lecture notes by Jochen Denzler |
| title_full | Teichmüller theory in Riemannian geometry based on lecture notes by Jochen Denzler Anthony J. Tromba |
| title_fullStr | Teichmüller theory in Riemannian geometry based on lecture notes by Jochen Denzler Anthony J. Tromba |
| title_full_unstemmed | Teichmüller theory in Riemannian geometry based on lecture notes by Jochen Denzler Anthony J. Tromba |
| title_short | Teichmüller theory in Riemannian geometry |
| title_sort | teichmuller theory in riemannian geometry based on lecture notes by jochen denzler |
| title_sub | based on lecture notes by Jochen Denzler |
| topic | Teichmüller, Espacios de Variedades Riemannianas Teichmüller-Raum (DE-588)4131425-6 gnd Riemannsche Geometrie (DE-588)4128462-8 gnd |
| topic_facet | Teichmüller, Espacios de Variedades Riemannianas Teichmüller-Raum Riemannsche Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003380571&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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