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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 | |