On graphic Bernstein type results in higher codimension

Wang, Mu-Tao

doi:10.1090/S0002-9947-02-03108-2

On graphic Bernstein type results in higher codimension
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by Mu-Tao Wang PDF

Trans. Amer. Math. Soc. 355 (2003), 265-271 Request permission

Abstract:

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

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