We prove, in all dimensions , that there exists a convex translator lying in a slab of width in (and in no smaller slab) if and only if . 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.
"On the existence of translating solutions of mean curvature flow in slab regions." Anal. PDE 13 (4) 1051 - 1072, 2020. https://doi.org/10.2140/apde.2020.13.1051