Entire scalar curvature flow and hypersurfaces of constant scalar curvature in Minkowski space. (English) Zbl 1180.53069

Bayard, Pierre

Methods Appl. Anal. 16, No. 1, 87-118 (2009).

Summary: 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.

MSC:

53C50	Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
35J60	Nonlinear elliptic equations
35K55	Nonlinear parabolic equations
53C44	Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010)

Keywords:

entire graphs; prescribed scalar curvature; scalar curvature flow; Minkowski space