Condition R and proper holomorphic maps between equidimensional product domains

2012/04/01 by Debraj Chakrabarti, Chakrabarti, Debraj, Kaushal Verma +1
Mathematics · #32H35 #Algebraic and Geometric Analysis #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #math.CV #msc:32H35

paper · pdf · doi:10.48550/arxiv.1204.0265

Some typos fixed in this final version. To appear in {\em Advances in Mathematics.}

openalex publication_date 2012/04/01 · arxiv created 2013/08/16 · arxiv updated 2013/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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