A collapsing ancient solution of mean curvature flow in R³

الأصل · EN

We construct a compact, convex ancient solution of mean curvature flow in Rⁿ⁺¹ with O(1)× O(n) symmetry that lies in a slab of width π. 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 π and in no smaller slab.