Harmonic maps, conservation laws, and moving frames:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English French |
| Veröffentlicht: |
Cambridge ; New York ; Melbourne ; Madrid ; Cape Town ; Singapor ; São Paulo ; Delhi ; Mexico City
Cambridge University Press
2002
|
| Ausgabe: | Second edition |
| Schriftenreihe: | Cambridge tracts in mathematics
150 |
| Schlagworte: | |
| Online-Zugang: | Sample text Publisher description Table of contents Inhaltsverzeichnis |
| Beschreibung: | xxv, 264 Seiten |
| ISBN: | 9780521811606 0521811600 |
Internformat
MARC
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| 240 | 1 | 0 | |a Applications harmoniques, lois de conservation et repères mobiles |
| 245 | 1 | 0 | |a Harmonic maps, conservation laws, and moving frames |c Frédéric Hélein (Ecole Normale Supérieure de Cachan) |
| 250 | |a Second edition | ||
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Datensatz im Suchindex
| _version_ | 1804129401061769216 |
|---|---|
| adam_text | Contents
Foreword page ix
Introduction xiii
Acknowledgements xxii
Notation xxiii
1 Geometric and analytic setting 1
1.1 The Laplacian on (M,g) 2
1.2 Harmonic maps between two Riemannian manifolds 5
1.3 Conservation laws for harmonic maps 11
1.3.1 Symmetries on J f 12
1.3.2 Symmetries on M: the stress energy tensor 18
1.3.3 Consequences of theorem 1.3.6 24
1.4 Variational approach: Sobolev spaces 31
1.4.1 Weakly harmonic maps 37
1.4.2 Weakly Noether harmonic maps 42
1.4.3 Minimizing maps 42
1.4.4 W eakly stationary maps 43
1.4.5 Relation between these different definitions 43
1.5 Regularity of weak solutions 46
2 Harmonic maps with symmetry 49
2.1 Backlund transformation 50
2.1.1 S^ valued maps 50
2.1.2 Maps taking values in a sphere Sn, n 2 54
2.1.3 Comparison 56
2.2 Harmonic maps with values into Lie groups 58
2.2.1 Families of curvature free connections 65
2.2.2 The dressing 72
2.2.3 Uhlenbeck factorization for maps with values
in U{n) 77
vii
viii Contents
2.2.4 S^ action 79
2.3 Harmonic maps with values into homogeneous spaces 82
2.4 Synthesis: relation between the different formulations 95
2.5 Compactness of weak solutions in the weak topology 101
2.6 Regularity of weak solutions 109
3 Compensations and exotic function spaces 114
3.1 Wente s inequality 115
3.1.1 The inequality on a plane domain 115
3.1.2 The inequality on a Riemann surface 119
3.2 Hardy spaces 128
3.3 Lorentz spaces 135
3.4 Back to Wente s inequality 145
3.5 Weakly stationary maps with values into a sphere 150
4 Harmonic maps without symmetry 165
4.1 Regularity of weakly harmonic maps of surfaces 166
4.2 Generalizations in dimension 2 187
4.3 Regularity results in arbitrary dimension 193
4.4 Conservation laws for harmonic maps without sym¬
metry 205
4.4.1 Conservation laws 206
4.4.2 Isometric embedding of vector bundle valued
differential forms 211
4.4.3 A variational formulation for the case m =
n = 2 and p = 1 215
4.4.4 Hidden symmetries for harmonic maps on
surfaces? 218
5 Surfaces with mean curvature in L2 221
5.1 Local results 224
5.2 Global results 237
5.3 Willmore surfaces 242
5.4 Epilogue: Coulomb frames and conformal coordinates 244
References 254
Index 263
|
| any_adam_object | 1 |
| author | Hélein, Frédéric 1963- |
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| classification_rvk | SK 370 |
| ctrlnum | (OCoLC)47658893 (DE-599)BVBBV014627915 |
| dewey-full | 514/.74 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.74 |
| dewey-search | 514/.74 |
| dewey-sort | 3514 274 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Second edition |
| format | Book |
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| id | DE-604.BV014627915 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:04:33Z |
| institution | BVB |
| isbn | 9780521811606 0521811600 |
| language | English French |
| lccn | 2001043129 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009940099 |
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| physical | xxv, 264 Seiten |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Cambridge University Press |
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| series | Cambridge tracts in mathematics |
| series2 | Cambridge tracts in mathematics |
| spelling | Hélein, Frédéric 1963- Verfasser (DE-588)172705681 aut Applications harmoniques, lois de conservation et repères mobiles Harmonic maps, conservation laws, and moving frames Frédéric Hélein (Ecole Normale Supérieure de Cachan) Second edition Cambridge ; New York ; Melbourne ; Madrid ; Cape Town ; Singapor ; São Paulo ; Delhi ; Mexico City Cambridge University Press 2002 xxv, 264 Seiten txt rdacontent n rdamedia nc rdacarrier Cambridge tracts in mathematics 150 Applications harmoniques Riemann, Variétés de Harmonic maps Riemannian manifolds Erhaltungssatz (DE-588)4131214-4 gnd rswk-swf Rahmen Statistik (DE-588)4689005-1 gnd rswk-swf Harmonische Abbildung (DE-588)4023452-6 gnd rswk-swf Harmonische Abbildung (DE-588)4023452-6 s Erhaltungssatz (DE-588)4131214-4 s Rahmen Statistik (DE-588)4689005-1 s DE-604 Cambridge tracts in mathematics 150 (DE-604)BV000000001 150 http://www.loc.gov/catdir/samples/cam031/2001043129.html Sample text http://www.loc.gov/catdir/description/cam022/2001043129.html Publisher description http://www.loc.gov/catdir/toc/cam027/2001043129.html Table of contents HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009940099&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hélein, Frédéric 1963- Harmonic maps, conservation laws, and moving frames Cambridge tracts in mathematics Applications harmoniques Riemann, Variétés de Harmonic maps Riemannian manifolds Erhaltungssatz (DE-588)4131214-4 gnd Rahmen Statistik (DE-588)4689005-1 gnd Harmonische Abbildung (DE-588)4023452-6 gnd |
| subject_GND | (DE-588)4131214-4 (DE-588)4689005-1 (DE-588)4023452-6 |
| title | Harmonic maps, conservation laws, and moving frames |
| title_alt | Applications harmoniques, lois de conservation et repères mobiles |
| title_auth | Harmonic maps, conservation laws, and moving frames |
| title_exact_search | Harmonic maps, conservation laws, and moving frames |
| title_full | Harmonic maps, conservation laws, and moving frames Frédéric Hélein (Ecole Normale Supérieure de Cachan) |
| title_fullStr | Harmonic maps, conservation laws, and moving frames Frédéric Hélein (Ecole Normale Supérieure de Cachan) |
| title_full_unstemmed | Harmonic maps, conservation laws, and moving frames Frédéric Hélein (Ecole Normale Supérieure de Cachan) |
| title_short | Harmonic maps, conservation laws, and moving frames |
| title_sort | harmonic maps conservation laws and moving frames |
| topic | Applications harmoniques Riemann, Variétés de Harmonic maps Riemannian manifolds Erhaltungssatz (DE-588)4131214-4 gnd Rahmen Statistik (DE-588)4689005-1 gnd Harmonische Abbildung (DE-588)4023452-6 gnd |
| topic_facet | Applications harmoniques Riemann, Variétés de Harmonic maps Riemannian manifolds Erhaltungssatz Rahmen Statistik Harmonische Abbildung |
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| volume_link | (DE-604)BV000000001 |
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