A schlichtness theorem for envelopes of holomorphy
Abstract
Let Omega be a domain in C2. 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 Cn, n>2. Additionally, we show that the theorem cannot be generalized to provide information about domains in C2 whose envelopes are multiply sheeted.
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