Curvature properties of hypersurfaces (Q1881538)

In the paper under review, the curvature properties of the graph of a function defined on the whole \({\mathbb R}^n\) are considered. Let \(\| A \| \) be the length of the shape operator \(A\) of the graph. It is shown that \(\inf \| A \| =0\) if \(\| A \| \) is bounded and the usaual mean curvature does not change sign. It is also shown that the \(r\)-th mean curvature \(H_r\) is zero if \(\| A\| \) is bounded and \(H_r\) is constant.