A new stability notion of closed hypersurfaces in the hyperbolic space

DOI10.2969/jmsj/78317831zbMath1420.53070OpenAlexW2919500522MaRDI QIDQ2317144

Henrique Fernandes de Lima, Arlandson Matheus Silva Oliveira, Jonatan Floriano da Silva, Marco Antonio L. Velásquez

Publication date: 8 August 2019

Published in: Journal of the Mathematical Society of Japan (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.jmsj/1551085233

zbMATH Keywords

geodesic sphereshyperbolic spacehigher-order mean curvaturesclosed hypersurfacesstrong \((r, k, a, b)\)-stability

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) Global submanifolds (53C40)

Cites Work

• Unnamed Item
• Strongly stable linear Weingarten hypersurfaces immersed in the hyperbolic space
• On the Gauss map of complete CMC hypersurfaces in the hyperbolic space
• Stability of hypersurfaces with constant mean curvature
• Stability of hypersurfaces of constant mean curvature in Riemannian manifolds
• Hypersurfaces with constant scalar curvature
• Uniqueness of spacelike hypersurfaces of constant mean curvature in foliated spacetimes
• Stable hypersurfaces with constant scalar curvature
• On the first eigenvalue of the linearized operator of the \(r\)-th mean curvature of a hypersurface
• Stability of hypersurfaces with constant \(r\)-mean curvature
• Integral formulas for compact space-like hypersurfaces in de Sitter space: Applications to the case of constant higher order mean curvature
• On the stability of hypersurfaces in space forms
• The stability of hypersurfaces revisited
• Compact graphs over a sphere of constant second order mean curvature
• Unicity of constant mean curvature hypersurfaces in some riemannian manifolds