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

摘要

Hypersurfaces of euclidean spaces with vanishing r-mean curvature generalize minimal hypersurfaces (case r = 1) 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. [References: 15]