On graphic Bernstein type results in higher codimension

Mu-Tao Wang Columbia University

Differential Geometry mathscidoc:1608.10066

Transactions of the American Mathematical Society , 355, (1), 265-271, 2003
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
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@inproceedings{mu-tao2003on,
  title={On graphic Bernstein type results in higher codimension },
  author={Mu-Tao Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160822221016010859383},
  booktitle={Transactions of the American Mathematical Society },
  volume={355},
  number={1},
  pages={265-271},
  year={2003},
}
Mu-Tao Wang. On graphic Bernstein type results in higher codimension . 2003. Vol. 355. In Transactions of the American Mathematical Society . pp.265-271. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160822221016010859383.
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