A note on the stability for constant higher mean curvature hypersurfaces in a Riemannian manifold

We give a notion of stability for constant r-mean curvature hypersurfaces in a general Riemannian manifold. When the ambient manifold is a space form, our notion coincide with the variational one \cite{BC} and when r=1, it coincides with the classic one for constant mean curvature hypersurfaces.Comment: We added a section where we introduce a symmetrized r-stability operato