Classification of Semigraphical Translators
Differential Geometry
2026-03-18 v2 Analysis of PDEs
Abstract
We complete the classification of semigraphical translators for mean curvature flow in that was initiated by Hoffman-Mart\'in-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-Rad\'o theory for translators and an angular maximum principle.
Cite
@article{arxiv.2411.16889,
title = {Classification of Semigraphical Translators},
author = {Francisco Martín and Mariel Sáez and Raphael Tsiamis and Brian White},
journal= {arXiv preprint arXiv:2411.16889},
year = {2026}
}
Comments
13 pages, 2 figures. This paper supersedes the preprint arXiv:2310.06980. Final version to appear in Crelle