On the Entropies of Hypersurfaces with bounded mean curvature

We are interested in the impact of entropies on the geometry of a hypersurface of a Rie- mannian 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 satised. This depends on the existence of an embedded tube around such hypersurface. Among the con- sequences 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.