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

Theodora Bourni, Mat Langford, Giuseppe Tinaglia

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)1051-1072
Number of pages22
JournalAnalysis & pde
Volume13
Issue number4
DOIs
Publication statusPublished - 13 Jun 2020

Keywords

  • Ancient solutions
  • Mean curvature flow
  • Translators

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