English

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 R3\mathbb{R}^3 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

R2 v1 2026-06-28T20:12:15.661Z