Examples of $H$-hypersurfaces in $H^n \times R$ and geometric applications

zbMath1203.53053arXiv0902.1623MaRDI QIDQ3560619

Ricardo Sa Earp, Pierre H. Bérard

Publication date: 14 May 2010

Full work available at URL: https://arxiv.org/abs/0902.1623

zbMATH Keywords

submanifoldsconstant mean curvaturehypersurfaces of product manifolds

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

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Rotational surfaces with prescribed mean curvature in \(\mathbb{H}^2 \times \mathbb{R}\) ⋮ Minimal hypersurfaces in \(\mathbb {H}^n \times \mathbb {R}\), total curvature and index ⋮ A Bernstein type theorem in \(\mathbb R\times\mathbb H^n\) ⋮ Constructions of \(H_r\)-hypersurfaces, barriers and Alexandrov theorem in \(\mathbb H^n\times\mathbb R\) ⋮ A relation between height, area, and volume for compact constant mean curvature surfaces in \(\mathbb M^{2} \times \mathbb R\) ⋮ Constant mean curvature hypersurfaces in \(\mathbb{H}^n \times \mathbb{R}\) with small planar boundary ⋮ All solutions of the CMC-equation in \({\mathbb H^n\times\mathbb R}\) invariant by parabolic screw motion ⋮ Geometric barriers for the existence of hypersurfaces with prescribed curvatures in \(\mathbb M^n\times\mathbb R\) ⋮ Hypersurfaces of constant higher-order mean curvature in \(M\times{\mathbb{R}}\) ⋮ Sharp solvability criteria for Dirichlet problems of mean curvature type in Riemannian manifolds: non-existence results

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