A local extension theorem for proper holomorphic mappings in C^2
Complex Variables
2007-05-23 v1
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.
Cite
@article{arxiv.math/0209411,
title = {A local extension theorem for proper holomorphic mappings in C^2},
author = {Rasul Shafikov and Kaushal Verma},
journal= {arXiv preprint arXiv:math/0209411},
year = {2007}
}
Comments
18 pages