A schlichtness theorem for envelopes of holomorphy

Daniel Jupiter

doi:10.1007/s00209-005-0927-1

A schlichtness theorem for envelopes of holomorphy

Daniel Jupiter

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Let Ω be a domain in ℂ². 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 ℂⁿ, n > 2. Additionally, we show that the theorem cannot be generalized to provide information about domains in ℂ² whose envelopes are multiply sheeted.

Original language	English (US)
Pages (from-to)	623-633
Number of pages	11
Journal	Mathematische Zeitschrift
Volume	253
Issue number	3
DOIs	https://doi.org/10.1007/s00209-005-0927-1
State	Published - Jul 2006
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

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10.1007/s00209-005-0927-1

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abstract = "Let Ω be a domain in ℂ2. 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 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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AB - Let Ω be a domain in ℂ2. 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 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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A schlichtness theorem for envelopes of holomorphy

Abstract

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