Uniqueness of convex ancient solutions to mean curvature flow in higher dimensions

Abstract

In this paper, we consider noncompact ancient solutions to the mean curvature flow in ${\mathbb{R}}^{n+1}$ ($n\ge 3$) which are strictly convex, uniformly two-convex, and noncollapsed. We prove that such an ancient solution is a rotationally symmetric translating soliton.

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