Vol. 13, No. 4, 2020

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

Theodora Bourni, Mat Langford and Giuseppe Tinaglia

Vol. 13 (2020), No. 4, 1051–1072

We prove, in all dimensions n 2, that there exists a convex translator lying in a slab of width πsec𝜃 in n+1 (and in no smaller slab) if and only if 𝜃 [0, π 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.

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mean curvature flow, translators, ancient solutions
Mathematical Subject Classification 2010
Primary: 53A10
Received: 12 June 2018
Revised: 3 April 2019
Accepted: 18 April 2019
Published: 13 June 2020
Theodora Bourni
Department of Mathematics
University of Tennessee
Knoxville, TN
United States
Mat Langford
Department of Mathematics
University of Tennessee
Knoxville, TN
United States
Giuseppe Tinaglia
Department of Mathematics
King’s College London
United Kingdom