Stability of hypersurfaces with vanishing r-mean curvatures in euclidean spaces

DOI10.1515/crll.2003.006zbMath1093.53063OpenAlexW4244920241MaRDI QIDQ4793828

Maria Fernanda Elbert, Hilário Alencar, Manfredo Perdigão do Carmo

Publication date: 16 February 2003

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/crll.2003.006

zbMATH Keywords

\(r\)-th mean curvaturestability of hypersurfacescritical point of variation

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Related Items (21)

The Eigenvalues of a Class of Elliptic Differential Operators ⋮ On stable complete hypersurfaces with vanishing \(r\)-mean curvature ⋮ An extension of Takahashi theorem for the linearized operators of the higher order mean curvatures ⋮ Stable hypersurfaces with constant scalar curvature ⋮ Hypersurfaces with null higher order mean curvature ⋮ Eigenvalue estimates for a class of elliptic differential operators on compact manifolds ⋮ The hyper-surfaces with two linear dependent mean curvature functions in space forms ⋮ Remarks on Gap Theorems for Complete Hypersurfaces with Constant Scalar Curvature ⋮ The complete hyper-surfaces with zero scalar curvature in \(\mathbb{R}^{n+1}\) ⋮ New \(r\)-minimal hypersurfaces via perturbative methods ⋮ Conformal fields and the stability of leaves with constant higher order mean curvature ⋮ Stability of area-preserving variations in space forms ⋮ \(r\)-minimal submanifolds in space forms ⋮ Stable hypersurfaces with zero scalar curvature in Euclidean space ⋮ On stable hypersurfaces with vanishing scalar curvature ⋮ Cones in the Euclidean space with vanishing scalar curvature ⋮ Monotonicity inequalities for the \(r\)-area and a degeneracy theorem for \(r\)-minimal graphs ⋮ The 𝑟-stability of hypersurfaces with zero Gauss-Kronecker curvature ⋮ Inequalities for eigenvalues of elliptic operators in divergence form on Riemannian manifolds ⋮ The halfspace theorem for minimal hypersurfaces in regions bounded by minimal cones ⋮ On the stability of cones in \(\mathbb R^{n+1}\) with zero scalar curvature

Cites Work

• \(O(2)\times O(2)\)-invariant hypersurfaces with zero scalar curvature
• O(p + 1) x O(p + 1)-Invariant hypersurfaces with zero scalar curvature in euclidean space

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