{"title":"On the connectedness of the boundary of $q$-complete domains","authors":"Rafael B. Andrist","doi":"arxiv-2407.11897","DOIUrl":null,"url":null,"abstract":"The boundary of every relatively compact Stein domain in a complex manifold\nof dimension at least two is connected. No assumptions on the boundary\nregularity are necessary. The same proofs hold also for $q$-complete domains,\nand in the context of almost complex manifolds as well.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"32 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Complex Variables","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.11897","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
The boundary of every relatively compact Stein domain in a complex manifold
of dimension at least two is connected. No assumptions on the boundary
regularity are necessary. The same proofs hold also for $q$-complete domains,
and in the context of almost complex manifolds as well.
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