Entire scalar curvature flow and hypersurfaces of constant scalar curvature in Minkowski space

TL;DR

This paper establishes the existence and convergence of entire spacelike hypersurfaces with constant negative scalar curvature in Minkowski space, using scalar curvature flow and barrier methods.

Contribution

It introduces a method to construct entire hypersurfaces with prescribed lightlike directions and constant scalar curvature in Minkowski space, advancing geometric analysis techniques.

Findings

Existence of entire spacelike hypersurfaces with constant negative scalar curvature.

Construction of scalar curvature flow converging to such hypersurfaces.

Use of barriers and a priori estimates in the proofs.

Abstract

We prove existence in the Minkowski space of entire spacelike hypersurfaces with constant negative scalar curvature and given set of lightlike directions at infinity; we also construct the entire scalar curvature flow with prescribed set of lightlike directions at infinity, and prove that the flow converges to a spacelike hypersurface with constant scalar curvature. The proofs rely on barriers construction and a priori estimates.