On the singular set of stationary harmonic maps
- Cite this article as:
- Bethuel, F. Manuscripta Math (1993) 78: 417. doi:10.1007/BF02599324
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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 , 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 (, ).