A schlichtness theorem for envelopes of holomorphy

الأصل · EN

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.