manuscripta mathematica

, Volume 78, Issue 1, pp 417–443 | Cite as

On the singular set of stationary harmonic maps

  • Fabrice Bethuel


LetM andN be compact riemannian manifolds, andu a stationary harmonic map fromM toN. We prove thatH n−2 (Σ)=0, wheren=dimM and Σ is the singular set ofu. This is a generalization of a result of C. Evans [7], where this is proved in the special caseN is a sphere. We also prove that, ifu is a weakly harmonic map inW 1,n (M, N), thenu is smooth. This extends results of F. Hélein for the casen=2, or the caseN is a sphere ([9], [10]).


Hardy Space Differential Form Absolute Constant Compact Riemannian Manifold Monotonicity Formula 
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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Fabrice Bethuel
    • 1
    • 2
  1. 1.Centre de Mathématiques et de Leurs ApplicationsEcole Normale Supérieure de Cachan et CNRSCachan CedexFrance
  2. 2.Cerma-ENPCNoisy Le Grand CedexFrance

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