Uniqueness of the bowl soliton

TL;DR

This paper proves that the only noncollapsed, uniformly 2-convex translating soliton for the mean curvature flow is the rotationally symmetric bowl soliton, confirming a conjecture in arbitrary dimensions.

Contribution

It establishes the uniqueness of the bowl soliton among noncollapsed, uniformly 2-convex translating solitons, solving a conjecture by White and Wang.

Findings

Uniqueness of the bowl soliton under specified conditions

Confirmation of the White and Wang conjecture in arbitrary dimensions

Advancement in understanding mean curvature flow solitons

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.