The half-space property and entire positive minimal graphs in M x R

By H. Rosenberg, F. Schulze, J. Spruck. 2012

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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.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/ba6c7569e4559430293eee3a49087df93449eb6b