On graphic Bernstein type results in higher codimension

2002/02/01 by Mu-Tao Wang, Wang, Mu-Tao · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #math.AP #math.DG

paper · pdf · doi:10.48550/arxiv.math/0202011

arxiv created 2002/02/01 · arxiv updated 2009/11/30

Abstract

Let Σbe a minimal submanifold of \R^n+m that can be represented as the graph of a smooth map f:\Rⁿ-->\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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