A local extension theorem for proper holomorphic mappings in ℂ2
Kaushal Verma2003, Journal of Geometric Analysis
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Abstract
Let f : D → D ′ be a proper holomorphic mapping between bounded domains D, D ′ in C 2 . Let M, M ′ be open pieces on ∂D, ∂D ′ respectively that are smooth, real analytic and of finite type. Suppose that the cluster set of M under f is contained in M ′ . It is shown that f extends holomorphically across M . This can be viewed as a local version of the Diederich-Pinchuk extension result for proper mappings in C 2 .
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