  We are interested in the impact of entropies on the geometry of a
hypersurface of a Riemannian manifold. In fact, we will be able to compare the
volume entropy of a hypersurface with that of the ambient manifold, provided
some geometric assumption are satisfied. This depends on the existence of an
embedded tube around such hypersurface. Among the consequences of our study of
the entropies, we point out some new answers to a question of do Carmo on
stable Euclidean hypersurfaces of constant mean curvature.
