#### Vol. 13, No. 4, 2020

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

### Theodora Bourni, Mat Langford and Giuseppe Tinaglia

Vol. 13 (2020), No. 4, 1051–1072
##### Abstract

We prove, in all dimensions $n\ge 2$, that there exists a convex translator lying in a slab of width $\pi sec𝜃$ in ${ℝ}^{n+1}$ (and in no smaller slab) if and only if $𝜃\in \left[0,\frac{\pi }{2}\right]$. 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.

##### Keywords
mean curvature flow, translators, ancient solutions
Primary: 53A10