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| Preface | |
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| Introduction | |
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| Lagrangians and Poincare-Cartan Forms | |
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| Lagrangians and Contact Geometry | |
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| The Euler-Lagrange System | |
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| Variation of a Legendre Submanifold | |
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| Calculation of the Euler-Lagrange System | |
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| The Inverse Problem | |
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| Noether's Theorem | |
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| Hypersurfaces in Euclidean Space | |
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| The Contact Manifold over E[superscript n+1] | |
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| Euclidean-invariant Euler-Lagrange Systems | |
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| Conservation Laws for Minimal Hypersurfaces | |
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| The Geometry of Poincare-Cartan Forms | |
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| The Equivalence Problem for n = 2 | |
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| Neo-Classical Poincare-Cartan Forms | |
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| Digression on Affine Geometry of Hypersurfaces | |
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| The Equivalence Problem for n [greater than or equal] 3 | |
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| The Prescribed Mean Curvature System | |
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| Conformally Invariant Euler-Lagrange Systems | |
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| Background Material on Conformal Geometry | |
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| Flat Conformal Space | |
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| The Conformal Equivalence Problem | |
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| The Conformal Laplacian | |
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| Conformally Invariant Poincare-Cartan Forms | |
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| The Conformal Branch of the Equivalence Problem | |
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| Conservation Laws for [Delta]u = Cu[superscript n+2 / n-2] | |
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| The Lie Algebra of Infinitesimal Symmetries | |
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| Calculation of Conservation Laws | |
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| Conservation Laws for Wave Equations | |
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| Energy Density | |
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| The Conformally Invariant Wave Equation | |
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| Energy in Three Space Dimensions | |
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| Additional Topics | |
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| The Second Variation | |
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| A Formula for the Second Variation | |
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| Relative Conformal Geometry | |
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| Intrinsic Integration by Parts | |
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| Prescribed Mean Curvature, Revisited | |
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| Conditions for a Local Minimum | |
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| Euler-Lagrange PDE Systems | |
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| Multi-contact Geometry | |
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| Functionals on Submanifolds of Higher Codimension | |
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| The Betounes and Poincare-Cartan Forms | |
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| Harmonic Maps of Riemannian Manifolds | |
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| Higher-Order Conservation Laws | |
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| The Infinite Prolongation | |
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| Noether's Theorem | |
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| The K = -1 Surface System | |
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| Two Backlund Transformations | |