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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.

53E10 Flows related to mean curvature
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
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