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| Foreword | |
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| Introduction | |
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| Acknowledgements | |
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| Notation | |
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| Geometric and analytic setting | |
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| The Laplacian on (M, g) | |
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| Harmonic maps between two Riemannian manifolds | |
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| Conservation laws for harmonic maps | |
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| Symmetries on N | |
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| Symmetries on M: the stress-energy tensor | |
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| Consequences of theorem 1.3.6 | |
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| Variational approach: Sobolev spaces | |
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| Weakly harmonic maps | |
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| Weakly Noether harmonic maps | |
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| Minimizing maps | |
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| Weakly stationary maps | |
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| Relation between these different definitions | |
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| Regularity of weak solutions | |
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| Harmonic maps with symmetry | |
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| Backlund transformation | |
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| S[superscript 2]-valued maps | |
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| Maps taking values in a sphere S[superscript n], n [greater than or equal] 2 | |
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| Comparison | |
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| Harmonic maps with values into Lie groups | |
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| Families of curvature-free connections | |
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| The dressing | |
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| Uhlenbeck factorization for maps with values in U(n) | |
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| S[superscript 1]-action | |
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| Harmonic maps with values into homogeneous spaces | |
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| Synthesis: relation between the different formulations | |
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| Compactness of weak solutions in the weak topology | |
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| Regularity of weak solutions | |
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| Compensations and exotic function spaces | |
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| Wente's inequality | |
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| The inequality on a plane domain | |
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| The inequality on a Riemann surface | |
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| Hardy spaces | |
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| Lorentz spaces | |
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| Back to Wente's inequality | |
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| Weakly stationary maps with values into a sphere | |
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| Harmonic maps without symmetry | |
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| Regularity of weakly harmonic maps of surfaces | |
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| Generalizations in dimension 2 | |
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| Regularity results in arbitrary dimension | |
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| Conservation laws for harmonic maps without symmetry | |
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| Conservation laws | |
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| Isometric embedding of vector-bundle-valued differential forms | |
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| A variational formulation for the case m = n = 2 and p = 1 | |
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| Hidden symmetries for harmonic maps on surfaces? | |
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| Surfaces with mean curvature in L[superscript 2] | |
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| Local results | |
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| Global results | |
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| Willmore surfaces | |
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| Epilogue: Coulomb frames and conformal coordinates | |
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| References | |
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| Index | |