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In this paper, we consider the anisotropic -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 >0, if the initial hypersurface is complete noncompact and locally uniformly convex, then the solution of the flow exists for all positive time.
Pan et al. (Tue,) studied this question.