The half-space property and entire positive minimal graphs in M x R
Differential Geometry
2012-06-18 v1 Analysis of PDEs
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.
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Cite
@article{arxiv.1206.3499,
title = {The half-space property and entire positive minimal graphs in M x R},
author = {Harold Rosenberg and Felix Schulze and Joel Spruck},
journal= {arXiv preprint arXiv:1206.3499},
year = {2012}
}
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12 pages