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We address the asymptotic behavior of the $\alpha$-Gauss curvature flow, for$\alpha >1/2$, with initial data a complete non-compact convex hypersurfacewhich is contained in a cylinder of bounded cross section. We show that theflow converges, as $t \to +\infty$, locally smoothly to a translating solitonwhich is uniquely determined by the asymptotic cylinder of the initialhypersurface.

Convergence of Gauss curvature flows to translating solitons