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

Autor:	Bourni, Theodora, Langford, Mat, Tinaglia, Giuseppe
Rok vydání:	2018
Předmět:	Mathematics - Differential Geometry
Druh dokumentu:	Working Paper
Popis:	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 $\theta\in[0,\frac{\pi}{2}]$. 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. Comment: We have made some updates to the introduction. The mathematical content is unchanged from version 2
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1805.05173 Zobrazit plný text záznamu View this record from Arxiv