Abstract
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]).
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Bethuel, F. On the singular set of stationary harmonic maps. Manuscripta Math 78, 417–443 (1993). https://doi.org/10.1007/BF02599324
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DOI: https://doi.org/10.1007/BF02599324