Entire ${\sigma }_k$ curvature flow in Minkowski space

Abstract

In this paper, we study the ${\sigma }_k$ curvature flow of noncompact spacelike hypersurfaces in Minkowski space. We prove that if the initial hypersurface satisfies certain conditions, then the flow exists for all time. Moreover, we show that after rescaling, the flow converges to a self-expander.