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A local extension theorem for proper holomorphic mappings in C^2

Rasul Shafikov·Kaushal Verma
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Abstract

Let f be a proper holomorphic mapping between bounded domains D and D' in C^2. Let M, M' be open pieces on the boundaries of D and 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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Rasul Shafikov, Kaushal Verma. 2002-09-30. A local extension theorem for proper holomorphic mappings in C^2. https://arxiv.org/abs/math/0209411

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