A schlichtness theorem for envelopes of holomorphy |
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Authors: | Daniel Jupiter |
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Institution: | (1) Department of Mathematics, Texas A & M University, College Station, TX 77843-3368, USA |
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Abstract: | Let Ω be a domain in . We prove the following theorem. If the envelope of holomorphy of Ω is schlicht over Ω, then the envelope is in fact schlicht.
We provide examples showing that the conclusion of the theorem does not hold in , n>2. Additionally, we show that the theorem cannot be generalized to provide information about domains in whose envelopes are multiply sheeted. |
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Keywords: | 32D10 32A10 |
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