## Stability and singularities of harmonic maps into spheres |

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### Contents

Interdependence of Propositions | 2 |

Introduction | 15 |

Monotonicity and Blowup | 35 |

Copyright | |

3 other sections not shown

### Common terms and phrases

3-spheres 4-dimensional domain behavior bounded domain Chapter compact set compact subset conformal diffeomorphism conformal geometry conformal vector field coordinate system Corollary 1.2 critical points define the map Definition denote diffeomorphism Dirichlet energy functional discrete set domain in Rm E D A E(uo energies of smooth energy minimizing map Euler-Lagrange equation finite number G-orbit Hausdorff Hm+1 homotopic isolated singular point Lemma Lm+2 map x/\x mapping degree maps between spheres maps into spheres Math monic maps monotonicity identity non-constant non-negative integer obtain orthogonal matrix present monograph problem proof of Theorem prove Radon measure Remark Riemannian manifold Rn+1 satisfying Sing(u second variation singular set singularity of harmonic smooth harmonic map SO(m Sobolev map source manifold stable stationary harmonic stationary harmonic map tension field Theorem 1.9 Tohoku University uj converges vector bundle vector field Vu|2 dx weak stability weakly harmonic map weakly stable stationary