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Proper holomorphic mappings of balanced domains in C-n

Janardhanan, Jaikrishnan (2015) Proper holomorphic mappings of balanced domains in C-n. In: MATHEMATISCHE ZEITSCHRIFT, 280 (1-2). pp. 257-268.

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Official URL: http://dx.doi.org/10.1007/s00209-015-1421-z

Abstract

We extend a well-known result, about the unit ball, by H. Alexander to a class of balanced domains in . Specifically: we prove that any proper holomorphic self-map of a certain type of balanced, finite-type domain in , is an automorphism. The main novelty of our proof is the use of a recent result of Opshtein on the behaviour of the iterates of holomorphic self-maps of a certain class of domains. We use Opshtein's theorem, together with the tools made available by finiteness of type, to deduce that the aforementioned map is unbranched. The monodromy theorem then delivers the result.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the SPRINGER HEIDELBERG, TIERGARTENSTRASSE 17, D-69121 HEIDELBERG, GERMANY
Keywords: Balanced domains; Proper holomorphic maps; Alexander's theorem
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 15 Jun 2015 05:11
Last Modified: 15 Jun 2015 05:11
URI: http://eprints.iisc.ac.in/id/eprint/51635

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