On the construction of closed nonconvex nonsoliton ancient mean curvature flows

2019/11/13 by Bourni, Theodora, Langford, Mathew, Mramor, Alexander · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1911.05641

Abstract

We construct closed, embedded, ancient mean curvature flows in each dimension n≥ 2 with the topology of S¹ × 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)

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