Dirichlet problem for space-like hypersurfaces with prescribed scalar curvature in $\mathbb R^{n,1}$

Abstract

We study the Dirichlet problem for the fully nonlinear elliptic partial differential equation of second order expressing the prescription of the mth symmetric function of the principal curvatures of a spacelike hypersurface in the Minkowski space \(\mathbb R^{n,1}.\) We completely solve the prescribed lorentzian scalar curvature equation (m=2) in ambiant dimension 4, if the datas are strictly convex.