Evolution of graphs in hyperbolic space by their Gauss curvature.

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 R n 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. [ABSTRACT FROM AUTHOR]