Author | Xin, Yuanlong. author |
---|---|
Title | Geometry of Harmonic Maps [electronic resource] / by Yuanlong Xin |
Imprint | Boston, MA : Birkhรคuser Boston, 1996 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-4084-6 |
Descript | X, 246 p. online resource |
I. Introduction -- 1.1 Vector Bundles -- 1.2 Harmonic Maps -- 1.3 A Bochner Type Formula -- 1.4 Basic Properties of Harmonic Maps -- II. Conservation Law -- 2.1 Stress-Energy Tensor and Conservation Law -- 2.2 Monotonicity Formula -- 2.3 Applications of Conservation Law to Liouville type Theorems -- 2.4 Further Generalizations -- III. Harmonic Maps and Gauss Maps -- 3.1 Generalized Gauss Maps -- 3.2 Cone-like Harmonic Maps -- 3.3 Generalized Maximum Principle -- 3.4 Estimates of Image Diameter and its Applications -- 3.5 Gauss Image of a Space-Like Hypersurface in Minkowski Space -- 3.6 Gauss Image of a Space-Like Submanifold in Pseudo-Euclidean Space -- IV. Harmonic Maps and Holomorphic Maps -- 4.1 Partial Energies -- 4.2 Harmonicity of Holomorphic Maps -- 4.3 Holomorphicity of Harmonic Maps -- V. Existence, Nonexistence and Regularity -- 5.1 Direct Method of the Calculus of Variations -- 5.2 Regularity Theorems -- 5.3 Nonexistence and Existence -- 5.4 Regularity Results of Harmonic Maps into Positively Curved Manifolds -- VI. Equivariant Harmonic Maps -- 6.1 Riemannian Submersions and Equivariant Harmonic Maps -- 6.2 Reduction Theorems -- 6.3 Equivariant Variational Formulas -- 6.4 On Harmonic Representatives of ?m(Sm) -- 6.5 Harmonic Maps via Isoparametric Maps -- 6.6 Harmonic Maps of Projective Spaces -- 6.7 Equivariant Boundary Value Problems -- References