Uniqueness of convex ancient solutions to hypersurface flows

We show that every convex ancient solution of mean curvature flow with Type I curvature growth is either spherical, cylindrical, or planar. We then prove the corresponding statement for flows by a natural class of curvature functions which are convex or concave in the second fundamental form. Neither of these results assumes interior noncollapsing.

Automated summary

The study demonstrates that convex ancient solutions of mean curvature flow with Type I curvature growth are limited to being either spherical, cylindrical, or planar. It also proves a similar statement for flows described by a specific class of curvature functions that are convex or concave in the second fundamental form. These results do not require the assumption of non-collapsing interior.