Conservation Law

  • Yuanlong Xin
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 23)


By E. Noether’s famous theorem, if an integral in the calculus of variations has continuous one-parameter groups of symmetries, then a conservation law, or a first integral of the Euler-Lagrange equation for the integral, must be associated to each of such symmetries. A concrete stress-energy tensor for smooth maps has been found by P. Baird and J. Eells, who also explained its applications in the theory of harmonic maps [B-E]. This chapter is devoted to the relevant topics.


Vector Bundle Sectional Curvature Ricci Curvature Symmetric Domain Geodesic Ball 
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Copyright information

© Birkhäuser Boston 1996

Authors and Affiliations

  • Yuanlong Xin
    • 1
  1. 1.Institute of MathematicsFudan UniversityShanghaiChina

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