An estimate for the Gauss curvature of minimal surfaces in ${\mathbb{R}}^m$ whose Gauss map omits a set of hyperplanes

Abstract

We give an estimate of the Gauss curvature for minimal surfaces in ${\mathbb{R}}^m$ whose Gauss map omits more than $m(m+1)/2$ hyperplanes in ${\mathbb{P}}^{m-1}(\mathbb{C})$.