Translators of flows by powers of the Gauss curvature

Abstract

A -translator is a surface in Euclidean space that moves by translations in a spatial direction under the -flow, where K is the Gauss curvature and is a constant. We classify all -translators that are rotationally symmetric. In particular, we prove that for each there is a -translator intersecting orthogonally the rotation axis. We also describe all -translators invariant by a uniparametric group of helicoidal motions and the translators obtained by separation of variables.