A Bernstein type theorem for minimal hypersurfaces via Gauss maps

Abstract

Let $M$ be an $n$-dimensional smooth oriented complete embedded minimal hypersurface in ${\mathbb{R}}^{n+1}$ with Euclidean volume growth. We show that if the image under the Gauss map of $M$ avoids some neighborhood of a half-equator, then $M$ must be an affine hyperplane.

14 pages

Cited by in corpus (1)

• On the intersection of minimal hypersurfaces of $S^k$