On the construction of closed nonconvex nonsoliton ancient mean curvature flows

Abstract

We construct closed, embedded, ancient mean curvature flows in each dimension $n\ge 2$ with the topology of $S^1\times S^{n-1}$. 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 $n=2$)

11 pages. Comments welcome!