Rigidity of solitons of the Gauss curvature flow in Euclidean space

Abstract

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.