An approach to the regularity for stable-stationary harmonic maps

Deliang, Hsu

doi:10.1090/S0002-9939-05-07818-4

An approach to the regularity for stable-stationary harmonic maps
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Proc. Amer. Math. Soc. 133 (2005), 2805-2812 Request permission

Abstract:

In this paper we investigate the regularity of stable-stationary harmonic maps. By assuming that the target manifolds do not carry any stable harmonic $S^{2}$, we obtain some compactness results and regularity theorems. In particular, we prove that the Hausdorff dimension of the singular set of these maps cannot exceed $n-3$, and the dimension estimate is optimal.

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