Finite Möbius Groups, Minimal Immersions of Spheres, and Moduli:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
2002
|
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | "Spherical soap bubbles", isometric minimal immersions of round spheres into round spheres, or spherical immersions for short, belong to a fast growing and fascinating area between algebra and geometry. This theory has rich inteconnections with a variety of mathematical disciplines such as invariant theory, convex geometry, harmonic maps, and orthogonal multiplications. In this book, the author traces the development of the study of spherical minimal immersions over the past 30 plus years, including Takahashi's 1966 proof regarding the existence of isometric minimal immersions, DoCarmo and Wallach's study of the uniqueness of the standard minimal immersion in the seventies, and the mor recent study of the variety of spherical minimal immersions which have been obtained by the "equivariant construction" as SU(2)-orbits, first used by Mashimo in 1984 and then later by DeTurck and Ziller in 1992. In trying to make this monograph accessible not just to research mathematicians but mathematics graduate students as well, the author included sizeable pieces of material from upper level undergraduate courses, additional graduate level topics such as Felix Kleins classic treatise of the icosahedron, and a valuable selection of exercises at the end of each chapter |
| Beschreibung: | 1 Online-Ressource (XVI, 319 p) |
| ISBN: | 9781461300618 9781461265467 |
| ISSN: | 0172-5939 |
| DOI: | 10.1007/978-1-4613-0061-8 |
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| isbn | 9781461300618 9781461265467 |
| issn | 0172-5939 |
| language | English |
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| spelling | Toth, Gabor Verfasser aut Finite Möbius Groups, Minimal Immersions of Spheres, and Moduli by Gabor Toth New York, NY Springer New York 2002 1 Online-Ressource (XVI, 319 p) txt rdacontent c rdamedia cr rdacarrier Universitext 0172-5939 "Spherical soap bubbles", isometric minimal immersions of round spheres into round spheres, or spherical immersions for short, belong to a fast growing and fascinating area between algebra and geometry. This theory has rich inteconnections with a variety of mathematical disciplines such as invariant theory, convex geometry, harmonic maps, and orthogonal multiplications. In this book, the author traces the development of the study of spherical minimal immersions over the past 30 plus years, including Takahashi's 1966 proof regarding the existence of isometric minimal immersions, DoCarmo and Wallach's study of the uniqueness of the standard minimal immersion in the seventies, and the mor recent study of the variety of spherical minimal immersions which have been obtained by the "equivariant construction" as SU(2)-orbits, first used by Mashimo in 1984 and then later by DeTurck and Ziller in 1992. In trying to make this monograph accessible not just to research mathematicians but mathematics graduate students as well, the author included sizeable pieces of material from upper level undergraduate courses, additional graduate level topics such as Felix Kleins classic treatise of the icosahedron, and a valuable selection of exercises at the end of each chapter Mathematics Global analysis (Mathematics) Global differential geometry Differential Geometry Analysis Mathematik Sphäre (DE-588)4182221-3 gnd rswk-swf Modulraum (DE-588)4183462-8 gnd rswk-swf Minimale Immersion (DE-588)4120739-7 gnd rswk-swf Harmonische Abbildung (DE-588)4023452-6 gnd rswk-swf Sphäre (DE-588)4182221-3 s Minimale Immersion (DE-588)4120739-7 s Harmonische Abbildung (DE-588)4023452-6 s Modulraum (DE-588)4183462-8 s 1\p DE-604 https://doi.org/10.1007/978-1-4613-0061-8 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Toth, Gabor Finite Möbius Groups, Minimal Immersions of Spheres, and Moduli Mathematics Global analysis (Mathematics) Global differential geometry Differential Geometry Analysis Mathematik Sphäre (DE-588)4182221-3 gnd Modulraum (DE-588)4183462-8 gnd Minimale Immersion (DE-588)4120739-7 gnd Harmonische Abbildung (DE-588)4023452-6 gnd |
| subject_GND | (DE-588)4182221-3 (DE-588)4183462-8 (DE-588)4120739-7 (DE-588)4023452-6 |
| title | Finite Möbius Groups, Minimal Immersions of Spheres, and Moduli |
| title_auth | Finite Möbius Groups, Minimal Immersions of Spheres, and Moduli |
| title_exact_search | Finite Möbius Groups, Minimal Immersions of Spheres, and Moduli |
| title_full | Finite Möbius Groups, Minimal Immersions of Spheres, and Moduli by Gabor Toth |
| title_fullStr | Finite Möbius Groups, Minimal Immersions of Spheres, and Moduli by Gabor Toth |
| title_full_unstemmed | Finite Möbius Groups, Minimal Immersions of Spheres, and Moduli by Gabor Toth |
| title_short | Finite Möbius Groups, Minimal Immersions of Spheres, and Moduli |
| title_sort | finite mobius groups minimal immersions of spheres and moduli |
| topic | Mathematics Global analysis (Mathematics) Global differential geometry Differential Geometry Analysis Mathematik Sphäre (DE-588)4182221-3 gnd Modulraum (DE-588)4183462-8 gnd Minimale Immersion (DE-588)4120739-7 gnd Harmonische Abbildung (DE-588)4023452-6 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Global differential geometry Differential Geometry Analysis Mathematik Sphäre Modulraum Minimale Immersion Harmonische Abbildung |
| url | https://doi.org/10.1007/978-1-4613-0061-8 |
| work_keys_str_mv | AT tothgabor finitemobiusgroupsminimalimmersionsofspheresandmoduli |