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Let $\sum$ be a minimal submanifold of $\mathbb{R}^{n+m}$ that can be represented as the graph of a smooth map $f : \mathbb{R}^n \to \mathbb{R}^m$. We apply a formula we derived in the study of mean curvature flow to obtain conditions under which $\sum$ must be an affine subspace. Our result covers all known ones in the general case. The conditions are stated in terms of the singular values of $df$.

mean curvature flow