Constant Mean Curvature Surfaces, Harmonic Maps and Integrable Systems
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser Basel
2001
|
| Schriftenreihe: | Lectures in Mathematics. ETH Zürich
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
MARC
| LEADER | 00000nam a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV042422099 | ||
| 003 | DE-604 | ||
| 005 | 20160405 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s2001 xx o|||| 00||| eng d | ||
| 020 | |a 9783034883306 |c Online |9 978-3-0348-8330-6 | ||
| 020 | |a 9783764365769 |c Print |9 978-3-7643-6576-9 | ||
| 024 | 7 | |a 10.1007/978-3-0348-8330-6 |2 doi | |
| 035 | |a (OCoLC)863718382 | ||
| 035 | |a (DE-599)BVBBV042422099 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 510 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Hélein, Frédéric |d 1963- |e Verfasser |0 (DE-588)172705681 |4 aut | |
| 245 | 1 | 0 | |a Constant Mean Curvature Surfaces, Harmonic Maps and Integrable Systems |c by Frédéric Hélein |
| 264 | 1 | |a Basel |b Birkhäuser Basel |c 2001 | |
| 300 | |a 1 Online-Ressource (122p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Lectures in Mathematics. ETH Zürich | |
| 500 | |a One of the most striking development of the last decades in the study of minimal surfaces, constant mean surfaces and harmonic maps is the discovery that many classical problems in differential geometry - including these examples - are actually integrable systems. This theory grew up mainly after the important discovery of the properties of the Korteweg-de Vries equation in the sixties. After C. Gardner, J. Greene, M. Kruskal et R. Miura [44] showed that this equation could be solved using the inverse scattering method and P. Lax [62] reinterpreted this method by his famous equation, many other deep observations have been made during the seventies, mainly by the Russian and the Japanese schools. In particular this theory was shown to be strongly connected with methods from algebraic geom etry (S. Novikov, V. B. Matveev, LM. Krichever. . . ), loop techniques (M. Adler, B. Kostant, W. W. Symes, M. J. Ablowitz . . . ) and Grassmannian manifolds in Hilbert spaces (M. Sato . . . ). Approximatively during the same period, the twist or theory of R. Penrose, built independentely, was applied successfully by R. Penrose and R. S. Ward for constructing self-dual Yang-Mills connections and four-dimensional self-dual manifolds using complex geometry methods. Then in the eighties it became clear that all these methods share the same roots and that other instances of integrable systems should exist, in particular in differential ge ometry. This led K. | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Mathematics, general | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Integrables System |0 (DE-588)4114032-1 |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 Fläche |0 (DE-588)4129864-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Konstante mittlere Krümmung |0 (DE-588)4235957-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Fläche |0 (DE-588)4129864-0 |D s |
| 689 | 0 | 1 | |a Konstante mittlere Krümmung |0 (DE-588)4235957-0 |D s |
| 689 | 0 | 2 | |a Harmonische Abbildung |0 (DE-588)4023452-6 |D s |
| 689 | 0 | 3 | |a Integrables System |0 (DE-588)4114032-1 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-0348-8330-6 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-027857516 | |
Datensatz im Suchindex
| DE-BY-TUM_katkey | 2069108 |
|---|---|
| _version_ | 1820806325402075136 |
| 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 | BV042422099 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863718382 (DE-599)BVBBV042422099 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-0348-8330-6 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03395nam a2200529zc 4500</leader><controlfield tag="001">BV042422099</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20160405 </controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s2001 xx o|||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783034883306</subfield><subfield code="c">Online</subfield><subfield code="9">978-3-0348-8330-6</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783764365769</subfield><subfield code="c">Print</subfield><subfield code="9">978-3-7643-6576-9</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-3-0348-8330-6</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)863718382</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042422099</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">510</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Hélein, Frédéric</subfield><subfield code="d">1963-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)172705681</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Constant Mean Curvature Surfaces, Harmonic Maps and Integrable Systems</subfield><subfield code="c">by Frédéric Hélein</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Basel</subfield><subfield code="b">Birkhäuser Basel</subfield><subfield code="c">2001</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (122p)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Lectures in Mathematics. ETH Zürich</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">One of the most striking development of the last decades in the study of minimal surfaces, constant mean surfaces and harmonic maps is the discovery that many classical problems in differential geometry - including these examples - are actually integrable systems. This theory grew up mainly after the important discovery of the properties of the Korteweg-de Vries equation in the sixties. After C. Gardner, J. Greene, M. Kruskal et R. Miura [44] showed that this equation could be solved using the inverse scattering method and P. Lax [62] reinterpreted this method by his famous equation, many other deep observations have been made during the seventies, mainly by the Russian and the Japanese schools. In particular this theory was shown to be strongly connected with methods from algebraic geom etry (S. Novikov, V. B. Matveev, LM. Krichever. . . ), loop techniques (M. Adler, B. Kostant, W. W. Symes, M. J. Ablowitz . . . ) and Grassmannian manifolds in Hilbert spaces (M. Sato . . . ). Approximatively during the same period, the twist or theory of R. Penrose, built independentely, was applied successfully by R. Penrose and R. S. Ward for constructing self-dual Yang-Mills connections and four-dimensional self-dual manifolds using complex geometry methods. Then in the eighties it became clear that all these methods share the same roots and that other instances of integrable systems should exist, in particular in differential ge ometry. This led K.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics, general</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Integrables System</subfield><subfield code="0">(DE-588)4114032-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Harmonische Abbildung</subfield><subfield code="0">(DE-588)4023452-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Fläche</subfield><subfield code="0">(DE-588)4129864-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Konstante mittlere Krümmung</subfield><subfield code="0">(DE-588)4235957-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Fläche</subfield><subfield code="0">(DE-588)4129864-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Konstante mittlere Krümmung</subfield><subfield code="0">(DE-588)4235957-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Harmonische Abbildung</subfield><subfield code="0">(DE-588)4023452-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="3"><subfield code="a">Integrables System</subfield><subfield code="0">(DE-588)4114032-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-3-0348-8330-6</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027857516</subfield></datafield></record></collection> |
| id | DE-604.BV042422099 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-24T04:23:24Z |
| institution | BVB |
| isbn | 9783034883306 9783764365769 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027857516 |
| oclc_num | 863718382 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (122p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Birkhäuser Basel |
| record_format | marc |
| series2 | Lectures in Mathematics. ETH Zürich |
| spellingShingle | Hélein, Frédéric 1963- Constant Mean Curvature Surfaces, Harmonic Maps and Integrable Systems Mathematics Mathematics, general Mathematik Integrables System (DE-588)4114032-1 gnd Harmonische Abbildung (DE-588)4023452-6 gnd Fläche (DE-588)4129864-0 gnd Konstante mittlere Krümmung (DE-588)4235957-0 gnd |
| subject_GND | (DE-588)4114032-1 (DE-588)4023452-6 (DE-588)4129864-0 (DE-588)4235957-0 |
| 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 by Frédéric Hélein |
| title_fullStr | Constant Mean Curvature Surfaces, Harmonic Maps and Integrable Systems by Frédéric Hélein |
| title_full_unstemmed | Constant Mean Curvature Surfaces, Harmonic Maps and Integrable Systems by Frédéric Hélein |
| title_short | Constant Mean Curvature Surfaces, Harmonic Maps and Integrable Systems |
| title_sort | constant mean curvature surfaces harmonic maps and integrable systems |
| topic | Mathematics Mathematics, general Mathematik Integrables System (DE-588)4114032-1 gnd Harmonische Abbildung (DE-588)4023452-6 gnd Fläche (DE-588)4129864-0 gnd Konstante mittlere Krümmung (DE-588)4235957-0 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Integrables System Harmonische Abbildung Fläche Konstante mittlere Krümmung |
| url | https://doi.org/10.1007/978-3-0348-8330-6 |
| work_keys_str_mv | AT heleinfrederic constantmeancurvaturesurfacesharmonicmapsandintegrablesystems |