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

In: Manfredo P. do Carmo – Selected Papers

Author

Listed:
  • Hilario Alencar

    (UFAL, Departamento de Matemática
    IMPA
    UFRJ, lnstituto de Matemätica)

  • Manfredo do Carmo

    (UFAL, Departamento de Matemática
    IMPA
    UFRJ, lnstituto de Matemätica)

  • Maria Fernanda Elbert

    (UFAL, Departamento de Matemática
    IMPA
    UFRJ, lnstituto de Matemätica)

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.

Suggested Citation

  • Hilario Alencar & Manfredo do Carmo & Maria Fernanda Elbert, 2012. "Stability of hypersurfaces with vanishing r-mean curvature in euclidean space," Springer Books, in: Keti Tenenblat (ed.), Manfredo P. do Carmo – Selected Papers, edition 127, pages 425-440, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-25588-5_31
    DOI: 10.1007/978-3-642-25588-5_31
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