Yeti doesn’t exist
Francisco Martín Universidad de Granada
We complete the classification of semigraphical translators for the mean curvature flow in \(\mathbb{R}^3\), a study initiated by Hoffman, Martín, and White. Specifically, we demonstrate that no solutions exist to the translator equation on the upper half-plane with alternating positive and negative infinite boundary values—a configuration previously referred to as the "Yeti". Furthermore, we establish the uniqueness of pitchfork and helicoid translators. Our proofs use Morse-Radó theory for translators and an angular maximum principle. This is joint work with Mariel Sáez, Raphael Tsiamis, and Brian White.