The “magic” of Weitzenböck formulas

  • Jean-Pierre Bourguignon
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 4)


In recent years, problems of geometric origin have attracted the attention of many analysts. In some instances, Geometry was pointing to the most subtle case of an analytic problem, e.g., the limiting case of Sobolev inequalities in the Yamabe problem or in Yang-Mills theory. Moreover, phenomena of a geometric nature were appearing in a P.D.E. context like the “bubbling off” phenomenon in the harmonic map problem. In many of the geometric situations considered, the problem could be reduced to solving an elliptic scalar equation, most often a non-linear one.


Scalar Curvature Ricci Curvature Compact Riemannian Manifold Einstein Metrics Principal Symbol 


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Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Jean-Pierre Bourguignon
    • 1
  1. 1.Centre de MathématiquesEcole PolytechniquePalaiseau CedexFrance

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