Entire convex curvature flow in Minkowski space

TL;DR

This paper investigates the evolution of noncompact spacelike hypersurfaces under convex curvature flow in Minkowski space, demonstrating long-term existence and convergence to a self-expanding hyperboloid.

Contribution

It establishes conditions for long-time existence and convergence of convex curvature flows in Minkowski space, extending understanding of geometric evolution in Lorentzian geometry.

Findings

Flow exists for all time under certain initial conditions.

Rescaled flow converges to a self-expanding hyperboloid.

Provides new insights into curvature flows in Minkowski space.

Abstract

In this paper, we study fully nonlinear curvature flows 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 the future timelike hyperboloid, which is a self-expander.