Stability of hypersurfaces with vanishing r-mean curvature in euclidean space

Hilario Alencar, Manfredo do Carmo () and Maria Fernanda Elbert
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Hilario Alencar: UFAL, Departamento de Matemática
Manfredo do Carmo: UFAL, Departamento de Matemática
Maria Fernanda Elbert: UFAL, Departamento de Matemática

A chapter in Manfredo P. do Carmo – Selected Papers, 2012, pp 425-440 from Springer

Abstract: Abstract Hypersurfaces of euclidean spaces with vanishing r-mean curvature generalize minimal hypersurfaces (case r = I) and include the important case of scalar curvature (r = 2). They are critical points of variational problems and a notion of stability can be assigned to them. When their defining equations are elliptic, we obtain a criterion for stability of bounded domains of such hypersurfaces that generalizes a known theorem of Barbosa and do Carmo for stability of minimal surfaces.

Keywords: Euclidean Space; Sectional Curvature; Jacobi Equation; Jacobi Operator; Minimal Hypersurface (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-25588-5_31

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DOI: 10.1007/978-3-642-25588-5_31

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