Application of the Complex Monge-Ampere equation to the study of proper   holomorphic mappings of strictly pseudoconvex domains
  We construct a special plurisubharmonic defining function for a smoothly bounded strictly pseudoconvex domain so that the determinant of the complex Hessian vanishes to high order on the boundary. This construction, coupled with regularity of solutions of complex Monge-Ampere equation and the reflection principle, enables us to give a new proof of the Fefferman mapping theorem. 
Steven G. Krantz and Song-Ying Li