Application of the Complex Monge-Ampere equation to the study of proper holomorphic mappings of strictly pseudoconvex domains

摘要

We construct a special plurisubharmonic defining function for a smoothlybounded strictly pseudoconvex domain so that the determinant of the complexHessian vanishes to high order on the boundary. This construction, coupled withregularity of solutions of complex Monge-Ampere equation and the reflectionprinciple, enables us to give a new proof of the Fefferman mapping theorem.