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.

arXiv commentThis is the final published version

References in corpus (5)

• Rotational symmetry of self-similar solutions to the Ricci flow
• Mean curvature flow with surgery
• Self-shrinkers with a rotational symmetry
• Convex ancient solutions of the mean curvature flow
• Uniqueness of the bowl soliton

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• Uniqueness of asymptotically conical tangent flows
• Rotational symmetry of ancient solutions to the Ricci flow in higher dimensions
• Asymptotics near extinction for nonlinear fast diffusion on a bounded domain
• A nonexistence result for wing-like mean curvature flows in ${\mathbb{R}}^4$
• Mean convex mean curvature flow with free boundary
• Uniqueness of convex ancient solutions to mean curvature flow in ${\mathbb{R}}^3$
• Convexity of 2-convex translating solitons to the mean curvature flow in ${\mathbb{R}}^{n+1}$
• Classification of bubble-sheet ovals in ${\mathbb{R}}^4$
• Uniqueness of ancient compact non-collapsed solutions to the 3-dimensional Ricci flow
• Ancient solutions and translators of Lagrangian mean curvature flow
• O(2)-symmetry of 3D steady gradient Ricci solitons