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We prove that any complete immersed globally orientable uniformly 2-convextranslating soliton $\Sigma \subset \mathbb{R}^{n+1}$ for the mean curvatureflow is locally strictly convex. It follows that a uniformly 2-convex entiregraphical translating soliton in $\mathbb{R}^{n+1},\, n\geq 3 $ is theaxisymmetric "bowl soliton".

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