Hypersurfaces with \(H_{r+1}=0\) in \(\mathbb H^n\times\mathbb R\)

DOI10.1007/S00229-015-0794-YzbMath1343.53056arXiv1503.07489OpenAlexW1921933654MaRDI QIDQ5965203

Maria Fernanda Elbert, Barbara Nelli, Walcy Santos

Publication date: 2 March 2016

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1503.07489

zbMATH Keywords

hypersurfaceproduct space\(r\)-minimal

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Related Items (3)

Minimal hypersurfaces in \(\mathbb {H}^n \times \mathbb {R}\), total curvature and index ⋮ Poincaré type inequality for hypersurfaces and rigidity results ⋮ Hypersurfaces of constant higher-order mean curvature in \(M\times{\mathbb{R}}\)

Cites Work

• Unnamed Item
• Unnamed Item
• Minimal hypersurfaces in \(\mathbb {H}^n \times \mathbb {R}\), total curvature and index
• Two-ended \(r\)-minimal hypersurfaces in Euclidean space
• Uniqueness, symmetry, and embeddedness of minimal surfaces
• Uniqueness and nonexistence theorems for hypersurfaces with \(H_r=0\)
• Variational properties of functions of the mean curvatures for hypersurfaces in space forms
• The maximum principle for hypersurfaces with vanishing curvature functions
• Two-ended hypersurfaces with $H_r=0$
• Maximum principle and symmetry for minimal hypersurfaces in H^nxR
• Isometric immersions into $\mathbb {S}^n\times \mathbb {R}$ and $\mathbb {H}^n\times \mathbb {R}$ and applications to minimal surfaces
• Maximum principles for hypersurfaces with vanishing curvature functions in an arbitrary Riemannian manifold
• Two-ended hypersurfaces with zero scalar curvature

This page was built for publication: Hypersurfaces with \(H_{r+1}=0\) in \(\mathbb H^n\times\mathbb R\)