Randomized classification demonstrates uniqueness of pitchfork and helicoid translators.
We complete the classification of semigraphical translators for mean curvature flow in <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mi>𝐑</m:mi> <m:mn>3</m:mn> </m:msup> </m:math> {R³} that was initiated by Hoffman, Martín and 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.
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Martín et al. (2026) studied this question.