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

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

1996-12-13

arxiv.org/abs/math/9611202v1

Mathematics

Complex Variables

Scientific paper

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.

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