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Exterior Differential Systems and Euler-Lagrange Partial Differential Equations

By: Robert Bryant, Phillip Griffiths, Daniel Grossman

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Paperback | 1 July 2003 | Edition Number 1

At a Glance

Paperback
216 Pages

Edition Type
New edition

Dimensions(cm)
23.0 x 15.0 x 1.2

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In "Exterior Differential Systems, the authors present the results of their ongoing development of a theory of the geometry of differential equations, focusing especially on Lagrangians and Poincare-Cartan forms. They also cover certain aspects of the theory of exterior differential systems, which provides the language and techniques for the entire study. Because it plays a central role in uncovering geometric properties of differential equations, the method of equivalence is particularly emphasized. In addition, the authors discuss conformally invariant systems at length, including results on the classification and application of symmetries and conservation laws. The book also covers the Second Variation, Euler-Lagrange PDE systems, and higher-order conservation laws.
This timely synthesis of partial differential equations and differential geometry will be of fundamental importance to both students and experienced researchers working in geometric analysis.

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You Can Find This Book In

Non-Fiction Mathematics Calculus & Mathematical Analysis Differential Calculus & Equations Geometry Differential & Riemannian Geometry Miscellaneous Items

Preface	p. vii
Introduction	p. 1
Lagrangians and Poincare-Cartan Forms	p. 9
Lagrangians and Contact Geometry	p. 9
The Euler-Lagrange System	p. 15
Variation of a Legendre Submanifold	p. 15
Calculation of the Euler-Lagrange System	p. 16
The Inverse Problem	p. 18
Noether's Theorem	p. 22
Hypersurfaces in Euclidean Space	p. 29
The Contact Manifold over E[superscript n+1]	p. 29
Euclidean-invariant Euler-Lagrange Systems	p. 32
Conservation Laws for Minimal Hypersurfaces	p. 35
The Geometry of Poincare-Cartan Forms	p. 45
The Equivalence Problem for n = 2	p. 47
Neo-Classical Poincare-Cartan Forms	p. 60
Digression on Affine Geometry of Hypersurfaces	p. 66
The Equivalence Problem for n [greater than or equal] 3	p. 73
The Prescribed Mean Curvature System	p. 82
Conformally Invariant Euler-Lagrange Systems	p. 87
Background Material on Conformal Geometry	p. 88
Flat Conformal Space	p. 88
The Conformal Equivalence Problem	p. 93
The Conformal Laplacian	p. 101
Conformally Invariant Poincare-Cartan Forms	p. 105
The Conformal Branch of the Equivalence Problem	p. 110
Conservation Laws for [Delta]u = Cu[superscript n+2 / n-2]	p. 118
The Lie Algebra of Infinitesimal Symmetries	p. 119
Calculation of Conservation Laws	p. 121
Conservation Laws for Wave Equations	p. 126
Energy Density	p. 129
The Conformally Invariant Wave Equation	p. 131
Energy in Three Space Dimensions	p. 135
Additional Topics	p. 141
The Second Variation	p. 141
A Formula for the Second Variation	p. 141
Relative Conformal Geometry	p. 144
Intrinsic Integration by Parts	p. 147
Prescribed Mean Curvature, Revisited	p. 148
Conditions for a Local Minimum	p. 153
Euler-Lagrange PDE Systems	p. 158
Multi-contact Geometry	p. 159
Functionals on Submanifolds of Higher Codimension	p. 163
The Betounes and Poincare-Cartan Forms	p. 166
Harmonic Maps of Riemannian Manifolds	p. 172
Higher-Order Conservation Laws	p. 176
The Infinite Prolongation	p. 176
Noether's Theorem	p. 180
The K = -1 Surface System	p. 190
Two Backlund Transformations	p. 198
Table of Contents provided by Ingram. All Rights Reserved.

Exterior Differential Systems and Euler-Lagrange Partial Differential Equations

At a Glance

Paperback

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How to return your order

Defective items

You Can Find This Book In

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