Caccioppoli’s inequalities on constant mean curvature hypersurfaces in Riemannian Manifolds

We prove some Caccioppoli's inequalities for the traceless part of the second fundamental form of a complete, non compact, nite index, constant mean curvature hypersurface of a Riemannian manifold, satisfying some curvature conditions. This allows us to unify and clarify many results in the literature and to obtain some new results. For example, we prove that there is no stable, complete, non compact hypersurface in Rn+1; n 5; with constant mean curvature H 6= 0; provided that, for suitable p; the Lp-norm of the traceless part of second fundamental form satises some growth condition