Constant mean curvature surfaces, harmonic maps and integrable systems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel [u.a.]
Birkhäuser
2001
|
| Series: | Lectures in mathematics : ETH Zürich
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 122 S. |
| ISBN: | 3764365765 |
Staff View
MARC
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| 245 | 1 | 0 | |a Constant mean curvature surfaces, harmonic maps and integrable systems |c Frédéric Hélein. Notes taken by Roger Moser |
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Record in the Search Index
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| adam_text | Contents
Preface 7
1 Introduction:
Surfaces with prescribed mean curvature 9
2 From minimal surfaces and CMC surfaces
to harmonic maps 15
2.1 Minimal surfaces 16
2.2 Constant mean curvature surfaces 18
3 Variational point of view and Noether s theorem 22
4 Working with the Hopf differential 34
4.1 Appendix 39
5 The Gauss Codazzi condition 41
5.1 Appendix 50
6 Elementary twistor theory for harmonic maps 52
6.1 Appendix 60
7 Harmonic maps as an integrable system 63
7.1 Maps into spheres 63
7.2 Generalizations 68
7.3 A new setting: loop groups 71
7.4 Examples 74
8 Construction of finite type solutions 81
8.1 Preliminary: the Iwasawa decomposition (for £c) .... 81
8.2 Application to loop Lie algebras 83
8.3 The algorithm 84
8.4 Some further properties of finite type solutions 87
9 Constant mean curvature tori are of finite type 89
9.1 The result 89
9.2 Appendix 94
6 Contents
10 Wente tori 107
10.1 CMC surfaces with planar curvature lines 107
10.2 A system of commuting ordinary equations 109
10.3 Recovering a finite type solution 110
10.4 Spectral curves Ill
11 Weierstrass type representations 112
11.1 Loop groups decompositions 112
11.2 Solutions in terms of holomorphic data 113
11.3 Meromorphic potentials 115
11.4 Generalizations 116
Bibliography 117
|
| any_adam_object | 1 |
| 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 | BV013746998 |
| callnumber-first | Q - Science |
| callnumber-label | QA645 |
| callnumber-raw | QA645 |
| callnumber-search | QA645 |
| callnumber-sort | QA 3645 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 370 |
| ctrlnum | (OCoLC)47045153 (DE-599)BVBBV013746998 |
| dewey-full | 516.3/62 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/62 |
| dewey-search | 516.3/62 |
| dewey-sort | 3516.3 262 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV013746998 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:51:18Z |
| institution | BVB |
| isbn | 3764365765 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009397679 |
| oclc_num | 47045153 |
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| physical | 122 S. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Birkhäuser |
| record_format | marc |
| series2 | Lectures in mathematics : ETH Zürich |
| spelling | Hélein, Frédéric 1963- Verfasser (DE-588)172705681 aut Constant mean curvature surfaces, harmonic maps and integrable systems Frédéric Hélein. Notes taken by Roger Moser Basel [u.a.] Birkhäuser 2001 122 S. txt rdacontent n rdamedia nc rdacarrier Lectures in mathematics : ETH Zürich GEOMETRIA DIFERENCIAL larpcal Harmonic maps Immersions (Mathematics) Surfaces of constant curvature Konstante mittlere Krümmung (DE-588)4235957-0 gnd rswk-swf Integrables System (DE-588)4114032-1 gnd rswk-swf Harmonische Abbildung (DE-588)4023452-6 gnd rswk-swf Fläche (DE-588)4129864-0 gnd rswk-swf Fläche (DE-588)4129864-0 s Konstante mittlere Krümmung (DE-588)4235957-0 s Harmonische Abbildung (DE-588)4023452-6 s Integrables System (DE-588)4114032-1 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009397679&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hélein, Frédéric 1963- Constant mean curvature surfaces, harmonic maps and integrable systems GEOMETRIA DIFERENCIAL larpcal Harmonic maps Immersions (Mathematics) Surfaces of constant curvature Konstante mittlere Krümmung (DE-588)4235957-0 gnd Integrables System (DE-588)4114032-1 gnd Harmonische Abbildung (DE-588)4023452-6 gnd Fläche (DE-588)4129864-0 gnd |
| subject_GND | (DE-588)4235957-0 (DE-588)4114032-1 (DE-588)4023452-6 (DE-588)4129864-0 |
| title | Constant mean curvature surfaces, harmonic maps and integrable systems |
| title_auth | Constant mean curvature surfaces, harmonic maps and integrable systems |
| title_exact_search | Constant mean curvature surfaces, harmonic maps and integrable systems |
| title_full | Constant mean curvature surfaces, harmonic maps and integrable systems Frédéric Hélein. Notes taken by Roger Moser |
| title_fullStr | Constant mean curvature surfaces, harmonic maps and integrable systems Frédéric Hélein. Notes taken by Roger Moser |
| title_full_unstemmed | Constant mean curvature surfaces, harmonic maps and integrable systems Frédéric Hélein. Notes taken by Roger Moser |
| title_short | Constant mean curvature surfaces, harmonic maps and integrable systems |
| title_sort | constant mean curvature surfaces harmonic maps and integrable systems |
| topic | GEOMETRIA DIFERENCIAL larpcal Harmonic maps Immersions (Mathematics) Surfaces of constant curvature Konstante mittlere Krümmung (DE-588)4235957-0 gnd Integrables System (DE-588)4114032-1 gnd Harmonische Abbildung (DE-588)4023452-6 gnd Fläche (DE-588)4129864-0 gnd |
| topic_facet | GEOMETRIA DIFERENCIAL Harmonic maps Immersions (Mathematics) Surfaces of constant curvature Konstante mittlere Krümmung Integrables System Harmonische Abbildung Fläche |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009397679&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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