The study shows how to foliate convex hypersurfaces in affine space with constant curvature.
problem Finding convex hypersurfaces with constant Gauss-Kronecker curvature in affine space.
method Solving a Monge-Ampère equation with specific boundary conditions.
result Regular domains in affine space are foliated by complete convex hypersurfaces with constant Gauss-Kronecker curvature.