## Journal of Differential Geometry

### The half-space property and entire positive minimal graphs in $M \times \mathbb{R}$.

#### Abstract

We show that a properly immersed minimal hypersurface in $M \times \mathbb{R}^+$ equals some $M \times\{c\}$ when $M$ is a complete, recurrent $n$-dimensional Riemannian manifold with bounded curvature. If on the other hand, $M$ is not necessarily recurrent but has nonnegative Ricci curvature with curvature bounded below, the same result holds for any positive entire minimal graph over $M$.

#### Article information

Source
J. Differential Geom., Volume 95, Number 2 (2013), 321-336.

Dates
First available in Project Euclid: 9 August 2013

https://projecteuclid.org/euclid.jdg/1376053449

Digital Object Identifier
doi:10.4310/jdg/1376053449

Mathematical Reviews number (MathSciNet)
MR3128986

Zentralblatt MATH identifier
1291.53075

#### Citation

Rosenberg, Harold; Schulze, Felix; Spruck, Joel. The half-space property and entire positive minimal graphs in $M \times \mathbb{R}$. J. Differential Geom. 95 (2013), no. 2, 321--336. doi:10.4310/jdg/1376053449. https://projecteuclid.org/euclid.jdg/1376053449