Abstract
In this paper, we consider the α-Gauss curvature flow for complete convex graphs over horosphere in the hyperbolic space. We show that for all positive power α>0, if the initial hypersurface is smooth, complete non-compact uniformly convex graph over Rn and bounded by two horospheres, then the solution of the flow exists for all time. Moreover, the evolution of horospheres act as barriers along the flow.
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