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

Abstract

In this paper, we investigate the convexity of mean convex asymptotically conical self-expanders to the mean curvature flow in $\mathbb{R}^{n+1}$. Specifically, for $n\geq 3$, we show that any $n$-dimensional complete mean convex self-expander asymptotic to mean convex and weakly convex cones must be strictly convex.