A Stability Criterion for Nonparametric Minimal Submanifolds

Abstract

An $n$ dimensional minimal submanifold $\Sigma$ of ${\mathbb{R}}^{n+m}$ is called non-parametric if $\Sigma$ can be represented as the graph of a vector-valued function $f:D\subset {\mathbb{R}}^n\mapsto {\mathbb{R}}^m$. This note provides a sufficient condition for the stability of such $\Sigma$ in terms of the norm of the differential $df$.

submitted