Boundary estimates of solutions for a class of Monge–Ampère equations.

On a smooth strictly convex bounded domain in R 2 , we establish some boundary estimates of the solution to the complete hyperbolic affine sphere equation. On the unit ball in R n , we also give some sharp estimates of the solutions of a class of Monge–Ampère equations. As an application, we prove the relative hyperbolic hypersurface constructed by solving two linked Monge–Ampère equations, has constant Gauss–Kronecker curvature and has bounded principal curvatures. [ABSTRACT FROM AUTHOR]