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

TY - JOUR

T1 - On the existence of translating solutions of mean curvature flow in slab regions

AU - Bourni, Theodora

AU - Langford, Mat

AU - Tinaglia, Giuseppe

PY - 2020/6/13

Y1 - 2020/6/13

N2 - We prove, in all dimensions n ≥ 2, that there exists a convex translator lying in a slab of width π sec θ in R n+1 (and in no smaller slab) if and only if θ ∈ [0,]. 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.

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

KW - Ancient solutions

KW - Mean curvature flow

KW - Translators

UR - http://www.scopus.com/inward/record.url?scp=85088088192&partnerID=8YFLogxK

U2 - 10.2140/apde.2020.13.1051

DO - 10.2140/apde.2020.13.1051

M3 - Article

SN - 2157-5045

VL - 13

SP - 1051

EP - 1072

JO - Analysis & pde

JF - Analysis & pde

IS - 4

ER -