The Bergman kernel function and proper holomorphic mappings

Bell, Steven R.

doi:10.1090/S0002-9947-1982-0645338-1

The Bergman kernel function and proper holomorphic mappings
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by Steven R. Bell PDF

Trans. Amer. Math. Soc. 270 (1982), 685-691 Request permission

Abstract:

It is proved that a proper holomorphic mapping $f$ between bounded complete Reinhardt domains extends holomorphically past the boundary and that if, in addition, ${f^{ - 1}}(0) = \{ 0\}$, then $f$ is a polynomial mapping. The proof is accomplished via a transformation rule for the Bergman kernel function under proper holomorphic mappings.

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On proper holomorphic mappings of strictly pseudoconvex domains

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