Convexity of mean convex asymptotically conical self-expanders to the mean curvature flow

In this paper, we prove that any $n$-dimensional complete mean convex self-expander of mean curvature flow in $\mathbb{R}^{n+1}$, $n\geq3$, asymptotic to weakly convex cones is strictly convex. As a consequence, each connected component of such a self-expander is properly embedded as an entire graph