On stable complete hypersurfaces with vanishing \(r\)-mean curvature

DOI10.2748/tmj/1113246548zbMath1062.53052OpenAlexW2033740414MaRDI QIDQ1885483

Manfredo Perdigão do Carmo, Maria Fernanda Elbert

Publication date: 5 November 2004

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2748/tmj/1113246548

zbMATH Keywords

finite total curvaturestable hypersurface\(r\)-mean curvature

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global submanifolds (53C40)

Related Items (4)

An extension of Takahashi theorem for the linearized operators of the higher order mean curvatures ⋮ The hyper-surfaces with two linear dependent mean curvature functions in space forms ⋮ \(r\)-minimal submanifolds in space forms ⋮ On stable hypersurfaces with vanishing scalar curvature

Cites Work

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• Variational properties of functions of the mean curvatures for hypersurfaces in space forms
• The maximum principle for hypersurfaces with vanishing curvature functions
• On stable surfaces of constant Gauss curvature in space forms
• The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature
• Shorter Notes: Globally Stable Complete Minimal Surfaces in R 3
• Stable complete minimal surfaces in 𝑅³ are planes
• On the Size of a Stable Minimal Surface in R 3
• Two-ended hypersurfaces with zero scalar curvature
• Stability of hypersurfaces with vanishing r-mean curvatures in euclidean spaces

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