Enclosure theorems for generalized mean curvature flows

Abstract.

We define a generalized notion of mean curvature for regular hypersurfaces in ${\mathbb R}^{n+1}$. This enables us to introduce a new class of geometric curvature flows for which we prove enclosure theorems, using methods of Dierkes [D] and Hildebrandt [H]. In particular, we obtain “neck-pinching” results that generalize previous observations by Ecker [E] concerning the classical mean curvature flow.