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

Junming Xie

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arXiv · 2509.01023

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

Junming Xie

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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.

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Junming Xie. 2025-08-31. Convexity of mean convex asymptotically conical self-expanders to the mean curvature flow. https://arxiv.org/abs/2509.01023

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