Convergence of Gauss curvature flows to translating solitons

2019/01/04 by Beomjun Choi, Kyeongsu Choi, Choi, Beomjun +3 · 2 citations
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1901.01080

Abstract

We address the asymptotic behavior of the α-Gauss curvature flow, for α>1/2, with initial data a complete non-compact convex hypersurface which is contained in a cylinder of 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.

Cited by

• Ancient Gauss Curvature Flows of Bounded Width
• Second boundary value problem for the Hessian curvature flow

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