In 46 page of Huisken, Gerhard, The volume preserving mean curvature flow, J. Reine Angew. Math. 382, 35-48 (1987). ZBL0621.53007.
Assume $M\subset \mathbb R^{n+1}$ is a n-dim compact smooth convex manifold without boundary, if the volume enclosed by $M$ is constant, how to show the principal curvature of $M$ can't tend to infinity? In fact, I think it is wrong, for example, in the picture below, the max principle curvature tend to infinity.
Besides, whether there are upper lower estimate of volume by the curvature of manifold?