Application of the Complex Monge–Ampère Equation to the Study of Proper Holomorphic Mappings of Strictly Pseudoconvex Domains
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–Ampère equation and the reflection principle, enables us to give a new proof of the Fefferman mapping theorem.