A note on area estimates for stable H-hypersurfaces and applications

We show some area estimates for stable CMC hypersurfaces which the ambient manifold haseither the scalar or sectional curvature bounded from below. In particular, we focus on immersions in three dimensional Riemannian manifolds. As application we derive upper estimates for the bottom spectrum of these hypersurfaces. The technique and most of our results are generalizations of the theorems obtained in [20] for stable minimal surfaces.