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Differential Geometrymathscidoc:1609.10333

Journal of Differential Geometry, 95, (2), 321-336, 2013
We show that a properly immersed minimal hypersurface in M × R+ equals some M×{c} when M is a complete, recurrent ndimensional 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.
@inproceedings{harold2013the,
title={The half-space property and entire positive minimal graphs in $M \times \mathbb{R}$.},
author={Harold Rosenberg, Felix Schulze, and Joel Spruck},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160914082659120834995},
booktitle={Journal of Differential Geometry},
volume={95},
number={2},
pages={321-336},
year={2013},
}

Harold Rosenberg, Felix Schulze, and Joel Spruck. The half-space property and entire positive minimal graphs in $M \times \mathbb{R}$.. 2013. Vol. 95. In Journal of Differential Geometry. pp.321-336. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160914082659120834995.