On the singular set of stationary harmonic maps
Thm. If \(n: M \to N\) is a stationary harmonic map between compact Riemannian manifolds, then its singular set has Hausdorff \((n-2)\)- dimensional measure, \(n = \dim M\). This was proved by [\textit{L. C. Evans}, Arch. Ration. Mech. Anal. 116, No. 2, 101-113 (1991; Zbl 0754.58007)] when \(N =S^ m\). Extending results of [\textit{F. Hélein}, Manuscr. Math. 70, No. 2, 203-218 (1991; Zbl 0718.58019)] the author proves the Theorem: If \(u\) is a weakly harmonic map in \(W^{1,n}(M,N)\), then \(u\) is smooth. The author's methods rely strongly on those of these two papers.
scientific article; zbMATH DE number 492742
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