In this paper, we consider λ-translating solitons and λ-shrinkers of the Gauss curvature flow in Euclidean space. We prove that planes and circular cylinders are the only λ-translating solitons with constant mean curvature. We also prove that planes, spheres and circular cylinders are the only λ-shrinkers with constant mean curvature. We give a classification of the λ-translating solitons and λ-shrinkers with one constant principal curvature.
Rafael López (Thu,) studied this question.