Condition R and proper holomorphic maps between equidimensional product domains

Details Condition R and proper holomorphic maps between equidimensional product domains Condition R and proper holomorphic maps between equidimensional product domains

2012-04-01

arxiv.org/abs/1204.0265v1

Mathematics

Complex Variables

Scientific paper

We consider proper holomorphic mappings of equidimensional pseudoconvex domains in complex Euclidean space, where both source and target can be represented as Cartesian products of smoothly bounded domains. It is shown that such mappings extend smoothly up to the closures of the domains, provided each factor of the source satis?es Condition R. It also shown that the number of smoothly bounded factors in the source and target must be the same, and the proper holomorphic map splits as product of proper mappings between the factor domains.

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