COLLAPSING ANCIENT SOLUTIONS OF MEAN CURVATURE FLOW

We construct a compact, convex ancient solution of mean curvature flow in Rn+1 with O(1) x O(n) symmetry that lies in a slab of width pi. We provide detailed asymptotics for this solution and show that, up to rigid motions, it is the only compact, convex, O(n)-invariant ancient solution that lies in a slab of width pi and in no smaller slab.

Automated summary

The paper presents a compact, convex ancient solution of mean curvature flow with specific symmetry, providing detailed asymptotics. It is shown to be the unique solution meeting certain criteria.