Author | Toth, Gabor. author |
---|---|
Title | Finite Mรถbius Groups, Minimal Immersions of Spheres, and Moduli [electronic resource] / by Gabor Toth |
Imprint | New York, NY : Springer New York : Imprint: Springer, 2002 |
Connect to | http://dx.doi.org/10.1007/978-1-4613-0061-8 |
Descript | XVI, 319 p. online resource |
1 Finite Mobius Groups -- 1.1 Platonic Solids and Finite Rotation Groups -- 1.2 Rotations and Mรถbius Transformations -- 1.3 Invariant Forms -- 1.4 Minimal Immersions of the 3-sphere into Spheres -- 1.5 Minimal Imbeddings of Spherical Space Forms into Spheres -- 1.6 Additional Topic: Kleinโs Theory of the Icosahedron -- 2 Moduli for Eigenmaps -- 2.1 Spherical Harmonics -- 2.2 Generalities on Eigenmaps -- 2.3 Moduli -- 2.4 Raising and Lowering the Degree -- 2.5 Exact Dimension of the Moduli ?p -- 2.6 Equivariant Imbedding of Moduli -- 2.7 Quadratic Eigenmaps in Domain Dimension Three -- 2.8 Raising the Domain Dimension -- 2.9 Additional Topic: Quadratic Eigenmaps -- 3 Moduli for Spherical Minimal Immersions -- 3.1 Conformal Eigenmaps and Moduli -- 3.2 Conformal Fields and Eigenmaps -- 3.3 Conformal Fields and Raising and Lowering the Degree -- 3.4 Exact Dimension of the Moduli ?p -- 3.5 Isotropic Minimal Immersions -- 3.6 Quartic Minimal Immersions in Domain Dimension Three -- 3.7 Additional Topic: The Inverse of ? -- 4 Lower Bounds on the Range of Spherical Minimal Immersions -- 4.1 Infinitesimal Rotations of Eigenmaps -- 4.2 Infinitesimal Rotations and the Casimir Operator -- 4.3 Infinitesimal Rotations and Degree-Raising -- 4.4 Lower Bounds for the Range Dimension, Part I -- 4.5 Lower Bounds for t he Range Dimension, Part II -- 4.6 Additional Topic: Operators -- Appendix 1. Convex Sets -- Appendix 2. Harmonic Maps and Minimal Immersions -- Appendix 3. Some Facts from the Representation Theory of the Special Orthogonal Group -- Glossary of Notations