On the singular set of stationary harmonic maps |
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| Authors: | Fabrice Bethuel |
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| Institution: | (1) Centre de Mathématiques et de Leurs Applications, Ecole Normale Supérieure de Cachan et CNRS, 61 Avenue du Président Wilson, 94235 Cachan Cedex, France;(2) Cerma-ENPC, La Courtine, 93167 Noisy Le Grand Cedex, France |
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| 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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| Keywords: | |
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