On the Construction of Closed Nonconvex Nonsoliton Ancient Mean Curvature Flows

We construct closed, embedded, ancient mean curvature flows in each dimension n≥ 2 with the topology of S¹× Sⁿ⁻¹. These examples are not mean convex and not solitons. They are constructed by analyzing perturbations of the self-shrinking doughnuts constructed by Drugan and Nguyen (or, alternatively, Angenent’s self-shrinking torus when $n =2$).