# zbMATH — the first resource for mathematics

On the existence of translating solutions of mean curvature flow in slab regions. (English) Zbl 1443.53053
Summary: 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 $$\theta \in \left[0, \frac{\pi}{2}\right]$$. 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.

##### MSC:
 53E10 Flows related to mean curvature 53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
##### Keywords:
mean curvature flow; translators; ancient solutions
Full Text: