Condition R and proper holomorphic maps between equidimensional product domains |
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Authors: | Debraj Chakrabarti Kaushal Verma |
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Affiliation: | 1. Department of Mathematics, Central Michigan University, Mt. Pleasant, MI 48859, USA;2. Department of Mathematics, Indian Institute of Science, Bengaluru 560012, India |
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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 a product of proper mappings between the factor domains. |
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Keywords: | 32H40 |
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