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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 has nonnegative Ricci curvature with curvature bounded below, the same result holds for any positive entire minimal graph over M. This is joint work with H. Rosenberg and J. Spruck.