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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On graphic Bernstein type results in higher codimension


Author: Mu-Tao Wang
Journal: Trans. Amer. Math. Soc. 355 (2003), 265-271
MSC (2000): Primary 53A10, 35J50, 53A07, 49Q05, 53C38
DOI: https://doi.org/10.1090/S0002-9947-02-03108-2
Published electronically: September 5, 2002
MathSciNet review: 1928088
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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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Additional Information

Mu-Tao Wang
Affiliation: Department of Mathematics, Columbia University, New York, New York 10027
Email: mtwang@math.columbia.edu

DOI: https://doi.org/10.1090/S0002-9947-02-03108-2
Received by editor(s): February 6, 2002
Published electronically: September 5, 2002
Additional Notes: The author was supported by NSF grant DMS 0104163.
Article copyright: © Copyright 2002 American Mathematical Society