Global smoothness for a singular Monge-Ampère equation

The global Cn+2,α-regularity for the graph of solutions to a singular Monge-Ampère equation was established in [7]. This equation arises in the study of hyperbolic affine spheres and is singular at the boundary. A compatibility condition for higher regularity was found in [7]. In this paper, we verify the compatibility condition and obtain the global C∞-regularity in the even dimensional case.