manuscripta mathematica

, Volume 78, Issue 1, pp 417–443

On the singular set of stationary harmonic maps

  • Fabrice Bethuel

DOI: 10.1007/BF02599324

Cite this article as:
Bethuel, F. Manuscripta Math (1993) 78: 417. doi:10.1007/BF02599324


LetM andN be compact riemannian manifolds, andu a stationary harmonic map fromM toN. We prove thatHn−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 inW1,n(M, N), thenu is smooth. This extends results of F. Hélein for the casen=2, or the caseN is a sphere ([9], [10]).

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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