APPLICATION OF THE COMPLEX MONGE-AMPÈRE EQUATION TO THE STUDY OF PROPER HOLOMORPHIC MAPPINGS OF STRICTLY PSEUDOCONVEX DOMAINS

STEVEN G. KRANTZ SONG-YING LI

Abstract. 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-Ampére equation and the reflection principle, enables us to give a new proof of the Fefferman mapping theorem.