Steven G. Krantz and Song-Ying Li
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-Amp\'ere equation and the reflection principle, enables us to give a new proof of the Fefferman mapping theorem.