On the maximal mean curvature of a smooth surface
  Given a smooth simply connected planar domain, the area is bounded away from zero in terms of the maximal curvature alone. We show that in higher dimensions this is not true, and for a given maximal mean curvature we provide smooth embeddings of the ball with arbitrary small volume. 
Vincenzo Ferone, Carlo Nitsch, Cristina Trombetti
math.OC math.DG