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On graphic Bernstein type results in higher codimension

Mu-Tao Wang
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Abstract

Let Σbe a minimal submanifold of \R^{n+m} that can be represented as the graph of a smooth map f:\R^n-->\R^m. We apply a formula we derived in the study of mean curvature flow to obtain conditions under which Σmust 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 $df$.

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Mu-Tao Wang. 2002-02-01. On graphic Bernstein type results in higher codimension. https://arxiv.org/abs/math/0202011

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