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

Felix Schulze; Harold Rosenberg; Joel Spruck

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

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arxiv 1206.3499 v1 pith:K3TZSUIX submitted 2012-06-15 math.DG math.AP

Harold Rosenberg , Felix Schulze , Joel Spruck This is my paper · ORCID

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keywords curvatureminimalboundedentirepositivebelowcompleteequals

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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.

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Half-Space Theorem for Minimal Hypersurfaces in $\mathbb{R}^4$
math.DG 2026-07 accept novelty 7.0 of 10

Complete properly embedded minimal hypersurfaces Σ³≅R³ in R⁴ with bounded curvature that lie in a slab (or half-space with cubic growth) are hyperplanes.

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