Open Access
October 2013 The half-space property and entire positive minimal graphs in $M \times \mathbb{R}$.
Harold Rosenberg, Felix Schulze, Joel Spruck
J. Differential Geom. 95(2): 321-336 (October 2013). DOI: 10.4310/jdg/1376053449


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 $M$.


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Harold Rosenberg. Felix Schulze. Joel Spruck. "The half-space property and entire positive minimal graphs in $M \times \mathbb{R}$.." J. Differential Geom. 95 (2) 321 - 336, October 2013.


Published: October 2013
First available in Project Euclid: 9 August 2013

zbMATH: 1291.53075
MathSciNet: MR3128986
Digital Object Identifier: 10.4310/jdg/1376053449

Rights: Copyright © 2013 Lehigh University

Vol.95 • No. 2 • October 2013
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