Harmonic maps, conservation laws, and moving frames:
The author presents an accessible and self-contained introduction to harmonic map theory and its analytical aspects, covering recent developments in the regularity theory of weakly harmonic maps. The book begins by introducing these concepts, stressing the interplay between geometry, the role of sym...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2002
|
| Ausgabe: | Second edition |
| Schriftenreihe: | Cambridge tracts in mathematics
150 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 UBR01 Volltext |
| Zusammenfassung: | The author presents an accessible and self-contained introduction to harmonic map theory and its analytical aspects, covering recent developments in the regularity theory of weakly harmonic maps. The book begins by introducing these concepts, stressing the interplay between geometry, the role of symmetries and weak solutions. The reader is then presented with a guided tour into the theory of completely integrable systems for harmonic maps, followed by two chapters devoted to recent results on the regularity of weak solutions. A self-contained presentation of 'exotic' functional spaces from the theory of harmonic analysis is given and these tools are then used for proving regularity results. The importance of conservation laws is stressed and the concept of a 'Coulomb moving frame' is explained in detail. The book ends with further applications and illustrations of Coulomb moving frames to the theory of surfaces |
| Beschreibung: | 1 Online-Ressource (xxv, 264 Seiten) |
| ISBN: | 9780511543036 |
| DOI: | 10.1017/CBO9780511543036 |
Internformat
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| 245 | 1 | 0 | |a Harmonic maps, conservation laws, and moving frames |c Frédéric Hélein |
| 246 | 1 | 3 | |a Harmonic Maps, Conservation Laws & Moving Frames |
| 250 | |a Second edition | ||
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 2002 | |
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| 490 | 0 | |a Cambridge tracts in mathematics |v 150 | |
| 505 | 8 | 0 | |g 1 |g 1 |t Geometric and analytic setting |g 1.1 |g 2 |t The Laplacian on (M, g) |g 1.2 |g 5 |t Harmonic maps between two Riemannian manifolds |g 1.3 |g 11 |t Conservation laws for harmonic maps |g 1.3.1 |g 12 |t Symmetries on N |g 1.3.2 |g 18 |t Symmetries on M: the stress-energy tensor |g 1.3.3 |g 24 |t Consequences of theorem 1.3.6 |g 1.4 |g 31 |t Variational approach: Sobolev spaces |g 1.4.1 |g 37 |t Weakly harmonic maps |g 1.4.2 |g 42 |t Weakly Noether harmonic maps |g 1.4.3 |g 42 |t Minimizing maps |g 1.4.4 |g 43 |t Weakly stationary maps |g 1.4.5 |g 43 |t Relation between these different definitions |g 1.5 |g 46 |t Regularity of weak solutions |g 2 |g 49 |t Harmonic maps with symmetry |g 2.1 |g 50 |t Backlund transformation |g 2.1.1 |g 50 |t S[superscript 2]-valued maps |g 2.1.2 |g 54 |t Maps taking values in a sphere S[superscript n], n [greater than or equal] 2 |g 2.1.3 |g 56 |t Comparison |g 2.2 |g 58 |t Harmonic maps with values into Lie groups |g 2.2.1 |
| 520 | |a The author presents an accessible and self-contained introduction to harmonic map theory and its analytical aspects, covering recent developments in the regularity theory of weakly harmonic maps. The book begins by introducing these concepts, stressing the interplay between geometry, the role of symmetries and weak solutions. The reader is then presented with a guided tour into the theory of completely integrable systems for harmonic maps, followed by two chapters devoted to recent results on the regularity of weak solutions. A self-contained presentation of 'exotic' functional spaces from the theory of harmonic analysis is given and these tools are then used for proving regularity results. The importance of conservation laws is stressed and the concept of a 'Coulomb moving frame' is explained in detail. The book ends with further applications and illustrations of Coulomb moving frames to the theory of surfaces | ||
| 650 | 4 | |a Harmonic maps | |
| 650 | 4 | |a Riemannian manifolds | |
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Datensatz im Suchindex
| _version_ | 1804176885067808768 |
|---|---|
| any_adam_object | |
| author | Hélein, Frédéric 1963- |
| author_GND | (DE-588)172705681 |
| author_facet | Hélein, Frédéric 1963- |
| author_role | aut |
| author_sort | Hélein, Frédéric 1963- |
| author_variant | f h fh |
| building | Verbundindex |
| bvnumber | BV043942368 |
| classification_rvk | SK 370 |
| collection | ZDB-20-CBO |
| contents | Geometric and analytic setting The Laplacian on (M, g) Harmonic maps between two Riemannian manifolds Conservation laws for harmonic maps Symmetries on N Symmetries on M: the stress-energy tensor Consequences of theorem 1.3.6 Variational approach: Sobolev spaces Weakly harmonic maps Weakly Noether harmonic maps Minimizing maps Weakly stationary maps Relation between these different definitions Regularity of weak solutions Harmonic maps with symmetry Backlund transformation S[superscript 2]-valued maps Maps taking values in a sphere S[superscript n], n [greater than or equal] 2 Comparison Harmonic maps with values into Lie groups |
| ctrlnum | (ZDB-20-CBO)CR9780511543036 (OCoLC)849910717 (DE-599)BVBBV043942368 |
| 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 |
| doi_str_mv | 10.1017/CBO9780511543036 |
| edition | Second edition |
| format | Electronic eBook |
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| id | DE-604.BV043942368 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:17Z |
| institution | BVB |
| isbn | 9780511543036 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029351338 |
| oclc_num | 849910717 |
| open_access_boolean | |
| owner | DE-12 DE-92 DE-355 DE-BY-UBR |
| owner_facet | DE-12 DE-92 DE-355 DE-BY-UBR |
| physical | 1 Online-Ressource (xxv, 264 Seiten) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO ZDB-20-CBO UBR Einzelkauf (Lückenergänzung CUP Serien 2018) |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | Cambridge tracts in mathematics |
| spelling | Hélein, Frédéric 1963- Verfasser (DE-588)172705681 aut Harmonic maps, conservation laws, and moving frames Frédéric Hélein Harmonic Maps, Conservation Laws & Moving Frames Second edition Cambridge Cambridge University Press 2002 1 Online-Ressource (xxv, 264 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 150 1 1 Geometric and analytic setting 1.1 2 The Laplacian on (M, g) 1.2 5 Harmonic maps between two Riemannian manifolds 1.3 11 Conservation laws for harmonic maps 1.3.1 12 Symmetries on N 1.3.2 18 Symmetries on M: the stress-energy tensor 1.3.3 24 Consequences of theorem 1.3.6 1.4 31 Variational approach: Sobolev spaces 1.4.1 37 Weakly harmonic maps 1.4.2 42 Weakly Noether harmonic maps 1.4.3 42 Minimizing maps 1.4.4 43 Weakly stationary maps 1.4.5 43 Relation between these different definitions 1.5 46 Regularity of weak solutions 2 49 Harmonic maps with symmetry 2.1 50 Backlund transformation 2.1.1 50 S[superscript 2]-valued maps 2.1.2 54 Maps taking values in a sphere S[superscript n], n [greater than or equal] 2 2.1.3 56 Comparison 2.2 58 Harmonic maps with values into Lie groups 2.2.1 The author presents an accessible and self-contained introduction to harmonic map theory and its analytical aspects, covering recent developments in the regularity theory of weakly harmonic maps. The book begins by introducing these concepts, stressing the interplay between geometry, the role of symmetries and weak solutions. The reader is then presented with a guided tour into the theory of completely integrable systems for harmonic maps, followed by two chapters devoted to recent results on the regularity of weak solutions. A self-contained presentation of 'exotic' functional spaces from the theory of harmonic analysis is given and these tools are then used for proving regularity results. The importance of conservation laws is stressed and the concept of a 'Coulomb moving frame' is explained in detail. The book ends with further applications and illustrations of Coulomb moving frames to the theory of surfaces Harmonic maps Riemannian manifolds Harmonische Abbildung (DE-588)4023452-6 gnd rswk-swf Rahmen Statistik (DE-588)4689005-1 gnd rswk-swf Erhaltungssatz (DE-588)4131214-4 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 Erscheint auch als Druck-Ausgabe 978-0-521-81160-6 https://doi.org/10.1017/CBO9780511543036 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Hélein, Frédéric 1963- Harmonic maps, conservation laws, and moving frames Geometric and analytic setting The Laplacian on (M, g) Harmonic maps between two Riemannian manifolds Conservation laws for harmonic maps Symmetries on N Symmetries on M: the stress-energy tensor Consequences of theorem 1.3.6 Variational approach: Sobolev spaces Weakly harmonic maps Weakly Noether harmonic maps Minimizing maps Weakly stationary maps Relation between these different definitions Regularity of weak solutions Harmonic maps with symmetry Backlund transformation S[superscript 2]-valued maps Maps taking values in a sphere S[superscript n], n [greater than or equal] 2 Comparison Harmonic maps with values into Lie groups Harmonic maps Riemannian manifolds Harmonische Abbildung (DE-588)4023452-6 gnd Rahmen Statistik (DE-588)4689005-1 gnd Erhaltungssatz (DE-588)4131214-4 gnd |
| subject_GND | (DE-588)4023452-6 (DE-588)4689005-1 (DE-588)4131214-4 |
| title | Harmonic maps, conservation laws, and moving frames |
| title_alt | Harmonic Maps, Conservation Laws & Moving Frames Geometric and analytic setting The Laplacian on (M, g) Harmonic maps between two Riemannian manifolds Conservation laws for harmonic maps Symmetries on N Symmetries on M: the stress-energy tensor Consequences of theorem 1.3.6 Variational approach: Sobolev spaces Weakly harmonic maps Weakly Noether harmonic maps Minimizing maps Weakly stationary maps Relation between these different definitions Regularity of weak solutions Harmonic maps with symmetry Backlund transformation S[superscript 2]-valued maps Maps taking values in a sphere S[superscript n], n [greater than or equal] 2 Comparison Harmonic maps with values into Lie groups |
| 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 |
| title_fullStr | Harmonic maps, conservation laws, and moving frames Frédéric Hélein |
| title_full_unstemmed | Harmonic maps, conservation laws, and moving frames Frédéric Hélein |
| title_short | Harmonic maps, conservation laws, and moving frames |
| title_sort | harmonic maps conservation laws and moving frames |
| topic | Harmonic maps Riemannian manifolds Harmonische Abbildung (DE-588)4023452-6 gnd Rahmen Statistik (DE-588)4689005-1 gnd Erhaltungssatz (DE-588)4131214-4 gnd |
| topic_facet | Harmonic maps Riemannian manifolds Harmonische Abbildung Rahmen Statistik Erhaltungssatz |
| url | https://doi.org/10.1017/CBO9780511543036 |
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