Complete translating solitons to the mean curvature flow in ${\mathbb{R}}^3$ with nonnegative mean curvature

Joel Spruck, Ling Xiao

We prove that any complete immersed two-sided mean convex translating soliton $\Sigma \subset {\mathbb{R}}^3$ for the mean curvature flow is convex. As a corollary it follows that an entir…