Abstract
We establish that any weakly conformal $$W^{1,2}$$ map from a Riemann surface S into a closed oriented sub-manifold $$N^n$$ of an euclidian space $${\mathbb {R}}^m$$ realizes, for almost every sub-domain, a stationary varifold if and only if it is a smooth conformal harmonic map form S into $$N^n$$ .
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