Uniqueness of the bowl soliton

Abstract

We prove that any translating soliton for the mean curvature flow which is noncollapsed and uniformly 2-convex must be the rotationally symmetric bowl soliton. In particular, this proves a conjecture of White and Wang, in the 2-convex case in arbitrary dimension.

References in corpus (3)

• Rotational symmetry of self-similar solutions to the Ricci flow
• Rotational Symmetry of Conical Kähler-Ricci Solitons
• Expanding Ricci Solitons Asymptotic to Cones

Cited by in corpus (9)

• Uniqueness of convex ancient solutions to mean curvature flow in higher dimensions
• Uniqueness of asymptotically conical tangent flows
• Rigidity results and topology at infinity of translating solitons of the mean curvature flow
• Bi-Halfspace and Convex Hull Theorems for Translating Solitons
• Convexity of 2-convex translating solitons to the mean curvature flow in ${\mathbb{R}}^{n+1}$
• Convexity of 2-convex translating and expanding solitons to the mean curvature flow in ${\mathbb{R}}^{n+1}$
• The atomic structure of ancient grain boundaries
• Rigidity and Curvature Estimates for Graphical Self-shrinkers
• A numerical stability analysis of mean curvature flow of noncompact hypersurfaces with Type-II curvature blowup