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arXiv · 1805.05173

On the existence of translating solutions of mean curvature flow in slab regions

Theodora Bourni·Mat Langford·Giuseppe Tinaglia
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Abstract

We prove, in all dimensions $n\geq 2$, that there exists a convex translator lying in a slab of width $\pi\sec\theta$ in $\mathbb{R}^{n+1}$ (and in no smaller slab) if and only if $\theta\in[0,\frac{\pi}{2}]$. We also obtain convexity and regularity results for translators which admit appropriate symmetries and study the asymptotics and reflection symmetry of translators lying in slab regions.

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Theodora Bourni, Mat Langford, Giuseppe Tinaglia. 2018-05-14. On the existence of translating solutions of mean curvature flow in slab regions. https://arxiv.org/abs/1805.05173

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