A schlichtness theorem for envelopes of holomorphy

Details A schlichtness theorem for envelopes of holomorphy A schlichtness theorem for envelopes of holomorphy

2004-04-27

arxiv.org/abs/math/0404497v3

Mathematics

Complex Variables

10 pages, final version for publication

Scientific paper

Let Omega be a domain in C^2. We prove the following theorem. If the envelope
of holomorphy of Omega is schlicht over Omega, then the envelope is in fact
schlicht. We provide examples showing that the theorem is not true in C^n, n>2.
Additionally, we show that the theorem cannot be generalized to provide
information about domains in C^2 whose envelopes are multiply sheeted.

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