Anisotropic Gauss curvature flow of complete non-compact graphs

In this paper, we consider the anisotropic $\alpha$-Gauss curvature flow for complete noncompact convex hypersurfaces in the Euclidean space with the anisotropy determined by a smooth closed uniformly convex Wulff shape. We show that for all positive power $\alpha>0$, if the initial hypersurface is complete noncompact and locally uniformly convex, then the solution of the flow exists for all positive time.