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.
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Alencar, H., Carmo, M.d., Elbert, M.F. (2012). Stability of hypersurfaces with vanishing r-mean curvature in euclidean space. In: Tenenblat, K. (eds) Manfredo P. do Carmo – Selected Papers. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25588-5_31
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DOI: https://doi.org/10.1007/978-3-642-25588-5_31
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