2004/04/27 by Daniel C. Jupiter, Daniel Jupiter, Jupiter, Daniel
Mathematics · #32A10 #32D10 #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematics and Applications #math.CV #msc:32A10 #msc:32D10
paper · pdf · doi:10.48550/arxiv.math/0404497
10 pages, final version for publication
openalex publication_date 2004/04/27 · arxiv created 2005/10/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.