Convergence of Gauss curvature flows to translating solitons

We address the asymptotic behavior of the alpha-Gauss curvature flow, for alpha > 1/2, with a complete non-compact convex initial hypersurface which is contained in a cylinder of a bounded cross section. We show that the flow converges, as t -> + infinity locally smoothly to a translating soliton which is uniquely determined by the asymptotic cylinder of the initial hypersurface. (c) 2022 Elsevier Inc. All rights reserved.

Automated summary

This study addresses the asymptotic behavior of the alpha-Gauss curvature flow with alpha > 1/2. The flow is shown to locally converge smoothly to a translating soliton, which is uniquely determined by the asymptotic cylinder of the initial hypersurface, as t tends to positive infinity.