Proper holomorphic mappings between hyperbolic product manifolds

Details Proper holomorphic mappings between hyperbolic product manifolds Proper holomorphic mappings between hyperbolic product manifolds

2011-05-13

arxiv.org/abs/1105.2648v1

Mathematics

Complex Variables

Scientific paper

We generalize a result of Remmert and Stein, on proper holomorphic mappings between domains that are products of certain planar domains, to finite proper holomorphic mappings between complex manifolds that are products of hyper- bolic Riemann surfaces. While an important special case of our result follows from the ideas developed by Remmert and Stein, our proof of the full result relies on the interplay of the latter ideas and a finiteness theorem for Riemann surfaces.

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