Nguyen's tridents and the classification of semigraphical translators for mean curvature flow

Abstract

We construct a one-parameter family of singly periodic translating solutions to mean curvature ow that converge as the period tends to 0 to the union of a grim reaper surface and a plane that bisects it lengthwise. The surfaces are semigraphical: they are properly embedded, and, after removing a discrete collection of vertical lines, they are graphs. We also provide a nearly complete classi cation of semigraphical translators.