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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.

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