The half-space property and entire positive minimal graphs in M x R

Abstract

We show that a properly immersed minimal hypersurface in M x R_+ equals some M x {c} when M is a complete, recurrent n-dimensional Riemannian manifold with bounded curvature. If on the other hand, M has nonnegative Ricci curvature with curvature bounded below, the same result holds for any positive entire minimal graph over M.

12 pages

References in corpus (1)

• A general halfspace theorem for constant mean curvature surfaces

Cited by in corpus (5)

• Spacelike hypersurfaces in standard static spacetimes
• A stability result for translating space-like graphs in Lorentz manifolds
• Translating solutions of the nonparametric mean curvature flow with nonzero Neumann boundary data in product manifold $M^n\times \mathbb{R}$
• Existence and uniqueness of solutions to the constant mean curvature equation with nonzero Neumann boundary data in product manifold $M^n\times \mathbb{R}$
• Stochastic half-space theorems for minimal surfaces and $H$-surfaces of ${\mathbb{R}}^3$