Curvature properties of hypersurfaces

Abstract.

In this paper we deal with curvature properties of hypersurfaces in an Euclidean space. We prove that an entire graph whose mean curvature does not change sign satisfies inf $\|A\| = 0$, if the length $\|A\|$ of the shape operator A is bounded. Moreover, we show that an entire graph with constant r-th mean curvature H _r satisfies $H_{r} = 0$, if the length $\|A\|$ of the shape operator A is bounded.