Uniqueness of two-convex closed ancient solutions to the mean curvature flow

Abstract

In this paper we consider the classification of closed non-collapsed ancient solutions to the Mean Curvature Flow $(n\ge 2)$ that are uniformly two-convex. We prove that they are either contracting spheres or they must coincide up to translations and scaling with the rotationally symmetric closed ancient non-collapsed solution first constructed by Brian White, and later by Robert Haslhofer and Or Hershkovits.