Convexity of 2-convex translating solitons to the mean curvature flow in ${\mathbb{R}}^{n+1}$

Abstract

We prove that any complete immersed globally orientable uniformly 2-convex translating soliton $\Sigma \subset {\mathbb{R}}^{n+1}$ for the mean curvature flow is locally strictly convex. It follows that a uniformly 2-convex entire graphical translating soliton in ${\mathbb{R}}^{n+1},n\ge 3$ is the axisymmetric "bowl soliton".

To be published on the Journal of Geometric Analysis

Cited by in corpus (1)

• Convexity of 2-convex translating and expanding solitons to the mean curvature flow in ${\mathbb{R}}^{n+1}$