Stability of Hypersurfaces with Constant r-Mean Curvature

Barbosa, João Lucas Marques
Colares, Antônio Gervasio

Departamento de Matemática, Universidade Federal do Ceará, Campus do Pici, 60455-760 Fortaleza-Ce, Brazil

E-mail: [email protected], [email protected])

Annals of Global Analysis and Geometry 15(3):p 277-297, June 1997.

We deal with compact hypersurfaces immersed in space forms with constant r-mean curvature. They are critical points for a variational problem. We show they are stable if and only if they are geodesic spheres, generalizing results on constant curvature hypersurfaces.