Classification of Semigraphical Translators

Abstract

We complete the classification of semigraphical translators for mean curvature flow in ${\mathbb{R}}^3$ that was initiated by Hoffman-Martín-White. Specifically, we show that there is no solution to the translator equation on the upper half-plane with alternating positive and negative infinite boundary values, and we prove the uniqueness of pitchfork and helicoid translators. The proofs use Morse-Radó theory for translators and an angular maximum principle.

13 pages, 2 figures. This paper supersedes the preprint arXiv:2310.06980. Final version to appear in Crelle