Harmonic maps, conservation laws, and moving frames:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2002
|
| Ausgabe: | 2nd ed |
| Schriftenreihe: | Cambridge tracts in mathematics
150 |
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Includes bibliographical references (p. 254-262) and index 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 N - 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 - Weakly 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[superscript 2]-valued maps - 50 -- - 2.1.2 - Maps taking values in a sphere S[superscript n], n [greater than or equal] 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 -- - 2.2.4 - S[superscript 1]-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 symmetry - 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 L[superscript 2] - 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 |
| Beschreibung: | 1 Online-Ressource (xxv, 264 p.) |
| ISBN: | 0511016603 0511543034 0521811600 9780511016608 9780511543036 9780521811606 |
Internformat
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| 100 | 1 | |a Hélein, Frédéric |d 1963- |e Verfasser |0 (DE-588)172705681 |4 aut | |
| 245 | 1 | 0 | |a Harmonic maps, conservation laws, and moving frames |c Frédéric Hélein |
| 250 | |a 2nd ed | ||
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 2002 | |
| 300 | |a 1 Online-Ressource (xxv, 264 p.) | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 0 | |a Cambridge tracts in mathematics |v 150 | |
| 500 | |a Includes bibliographical references (p. 254-262) and index | ||
| 500 | |a 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 N - 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 - Weakly 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[superscript 2]-valued maps - 50 -- - 2.1.2 - Maps taking values in a sphere S[superscript n], n [greater than or equal] 2 - 54 -- - 2.1.3 - Comparison - 56 -- - 2.2 - Harmonic maps with values into Lie groups - 58 -- - 2.2.1 | ||
| 500 | |a - 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 -- - 2.2.4 - S[superscript 1]-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 | ||
| 500 | |a - Regularity results in arbitrary dimension - 193 -- - 4.4 - Conservation laws for harmonic maps without symmetry - 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 L[superscript 2] - 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 | ||
| 650 | 7 | |a MATHEMATICS / Topology |2 bisacsh | |
| 650 | 4 | |a Applications harmoniques | |
| 650 | 4 | |a Riemann, Variétés de | |
| 650 | 7 | |a Erhaltungssatz |2 swd | |
| 650 | 7 | |a Harmonische Abbildung |2 swd | |
| 650 | 4 | |a Harmonic maps | |
| 650 | 4 | |a Riemannian manifolds | |
| 650 | 0 | 7 | |a Rahmen |g Statistik |0 (DE-588)4689005-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Harmonische Abbildung |0 (DE-588)4023452-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Erhaltungssatz |0 (DE-588)4131214-4 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804175583198838784 |
|---|---|
| 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 | BV043137578 |
| collection | ZDB-4-EBA |
| ctrlnum | (OCoLC)70748539 (DE-599)BVBBV043137578 |
| 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 | 2nd ed |
| format | Electronic eBook |
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| id | DE-604.BV043137578 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:18:35Z |
| institution | BVB |
| isbn | 0511016603 0511543034 0521811600 9780511016608 9780511543036 9780521811606 |
| language | English |
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| physical | 1 Online-Ressource (xxv, 264 p.) |
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| publishDate | 2002 |
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| 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 2nd ed Cambridge Cambridge University Press 2002 1 Online-Ressource (xxv, 264 p.) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 150 Includes bibliographical references (p. 254-262) and index 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 N - 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 - Weakly 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[superscript 2]-valued maps - 50 -- - 2.1.2 - Maps taking values in a sphere S[superscript n], n [greater than or equal] 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 -- - 2.2.4 - S[superscript 1]-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 symmetry - 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 L[superscript 2] - 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 MATHEMATICS / Topology bisacsh Applications harmoniques Riemann, Variétés de Erhaltungssatz swd Harmonische Abbildung swd Harmonic maps Riemannian manifolds Rahmen Statistik (DE-588)4689005-1 gnd rswk-swf Harmonische Abbildung (DE-588)4023452-6 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 1\p DE-604 http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=77949 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Hélein, Frédéric 1963- Harmonic maps, conservation laws, and moving frames MATHEMATICS / Topology bisacsh Applications harmoniques Riemann, Variétés de Erhaltungssatz swd Harmonische Abbildung swd Harmonic maps Riemannian manifolds Rahmen Statistik (DE-588)4689005-1 gnd Harmonische Abbildung (DE-588)4023452-6 gnd Erhaltungssatz (DE-588)4131214-4 gnd |
| subject_GND | (DE-588)4689005-1 (DE-588)4023452-6 (DE-588)4131214-4 |
| title | Harmonic maps, conservation laws, and moving frames |
| 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 | MATHEMATICS / Topology bisacsh Applications harmoniques Riemann, Variétés de Erhaltungssatz swd Harmonische Abbildung swd Harmonic maps Riemannian manifolds Rahmen Statistik (DE-588)4689005-1 gnd Harmonische Abbildung (DE-588)4023452-6 gnd Erhaltungssatz (DE-588)4131214-4 gnd |
| topic_facet | MATHEMATICS / Topology Applications harmoniques Riemann, Variétés de Erhaltungssatz Harmonische Abbildung Harmonic maps Riemannian manifolds Rahmen Statistik |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=77949 |
| work_keys_str_mv | AT heleinfrederic harmonicmapsconservationlawsandmovingframes |