Finite Möbius groups, minimal immersions of spheres, and moduli /
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| Author / Creator: | Tóth, Gábor, Ph. D. |
|---|---|
| Imprint: | New York : Springer, c2002. |
| Description: | xvi, 317 p. : ill. ; 24 cm. |
| Language: | English |
| Series: | Universitext |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/4601283 |
Table of Contents:
- 1. Finite Mobius Groups
- 1.1. Platonic Solids and Finite Rotation Groups
- 1.2. Rotations and Mobius 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: Klein's 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 L[superscript 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 M[superscript p]
- 3.5. Isotropic Minimal Immersions
- 3.6. Quartic Minimal Immersions in Domain Dimension Three
- 3.7. Additional Topic: The Inverse of [Psi]
- 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 the Range Dimension, Part II
- 4.6. Additional Topic: Operators. App. 1. Convex Sets
- App. 2. Harmonic Maps and Minimal Immersions
- App. 3. Some Facts from the Representation Theory of the Special Orthogonal Group.
