A Bernstein type theorem in \(\mathbb R\times\mathbb H^n\)

DOI10.1007/S00574-012-0003-5zbMath1276.53067OpenAlexW2045635753WikidataQ124851725 ScholiaQ124851725MaRDI QIDQ1935321

Henrique Fernandes de Lima, Ulisses L. Parente

Publication date: 14 February 2013

Published in: Bulletin of the Brazilian Mathematical Society. New Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00574-012-0003-5

zbMATH Keywords

mean curvaturecomplete hypersurfacevertical graph

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Geodesic flows in symplectic geometry and contact geometry (53D25) Local differential geometry of Lorentz metrics, indefinite metrics (53B30)

Related Items (7)

On Bernstein-type properties of complete hypersurfaces in weighted warped products ⋮ Rigidity of complete hypersurfaces in the Euclidean space via anisotropic mean curvatures ⋮ On the mean curvature flow solitons in Riemannian spaces endowed with a Killing vector field ⋮ Uniform a priori estimates for a class of horizontal minimal equations ⋮ On the unicity of complete hypersurfaces immersed in a semi-Riemannian warped product ⋮ On the angle of complete CMC hypersurfaces in Riemannian product spaces ⋮ On the geometry of submanifolds in certain warped products

Cites Work

• Complete constant mean curvature surfaces and Bernstein type theorems in \(\mathbb M^2 \times \mathbb R\)
• A Bernstein-type theorem for Riemannian manifolds with a Killing field
• Complete spacelike hypersurfaces with constant mean curvature in \(-\mathbb R\times \mathbb H^n\)
• Complete vertical graphs with constant mean curvature in semi-Riemannian warped products
• Minimal surfaces in \(M^2\times \mathbb{R}\)
• Isometric immersions of Riemannian manifolds
• Embedded positive constant r-mean curvature hypersurfaces in Mm × R
• Examples of $H$-hypersurfaces in $H^n \times R$ and geometric applications

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