Condition R and proper holomorphic maps between equidimensional product domains
Complex Variables
2013-08-19 v3
Abstract
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 satisfies 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.
Cite
@article{arxiv.1204.0265,
title = {Condition R and proper holomorphic maps between equidimensional product domains},
author = {Debraj Chakrabarti and Kaushal Verma},
journal= {arXiv preprint arXiv:1204.0265},
year = {2013}
}
Comments
Some typos fixed in this final version. To appear in {\em Advances in Mathematics.}