Stable constant mean curvature hypersurfaces

Let Nn+1 be a Riemannian manifold with sectional curvatures uniformly bounded from below. When n = 3, 4, we prove that there are no complete ( strongly) stable H-hypersurfaces, without boundary, provided vertical bar H vertical bar is large enough. In particular, we prove that there are no complete strongly stable H-hypersurfaces in Rn+1 without boundary, H not equal 0.