Convergence of Gauss curvature flows to translating solitons

Abstract

© 2022 Elsevier Inc.We address the asymptotic behavior of the α-Gauss curvature flow, for α>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→+∞, locally smoothly to a translating soliton which is uniquely determined by the asymptotic cylinder of the initial hypersurface.