A note on the isoperimetric dimension of a manifold (Q1978138)

Using the notion of the isoperimetric dimension introduced by M. Gromov the author gives another proof for a result of \textit{R. Hamilton} [Commun. Anal. Geom. 2, 167-172 (1994; Zbl 0843.53002)]: Let \(M\) be a smooth strictly convex complete hypersurface bounding a region in Euclidean space. Suppose that its second fundamental form is \(\varepsilon\)-pinched. Then \(M\) is compact. This may be used to prove Huisken's result on compact convex hypersurfaces shrinking under the mean curvature flow.