On the Gauss map of complete CMC hypersurfaces in the hyperbolic space

DOI10.1016/j.jmaa.2011.08.046zbMath1251.53035OpenAlexW2007400391MaRDI QIDQ643591

Henrique Fernandes de Lima, Cicero Pedro Aquino

Publication date: 2 November 2011

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2011.08.046

zbMATH Keywords

rigidityhyperbolic spaceconstant mean curvaturehypersurfaces

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

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Cites Work

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• On subharmonic functions and differential geometry in the large
• On hypersurfaces into Riemannian spaces of constant sectional curvature
• A characterization of quadric constant mean curvature hypersurfaces of spheres
• Complete vertical graphs with constant mean curvature in semi-Riemannian warped products
• Existence of constant mean curvature graphs in hyperbolic space
• Complete non-compact spacelike hypersurfaces of constant mean curvature in de Sitter spaces
• Integral formulas for compact space-like hypersurfaces in de Sitter space: Applications to the case of constant higher order mean curvature
• Uniqueness of constant mean curvature surfaces properly immersed in a slab
• Isometric immersions of Riemannian manifolds
• Local rigidity theorems for minimal hypersurfaces
• On the Gauss mapping for hypersurfaces of constant mean curvature in the sphere
• Harmonic functions on complete riemannian manifolds
• Complete Riemannian Manifolds and Some Vector Fields