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Mathematics > Complex Variables

arXiv:1805.00584 (math)
[Submitted on 2 May 2018 (v1), last revised 11 Oct 2018 (this version, v2)]

Title:Weakly complete domains in Grauert type surfaces

Authors:Samuele Mongodi
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Abstract:The aim of this short note is to investigate the geometry of weakly complete subdomains of Grauert type surfaces, i.e. open connected sets D, sitting inside a Grauert type surface X, which admit a smooth plurisubharmonic exhaustion function. We prove that they are either modifications of Stein spaces or Grauert type surfaces themselves and we apply these results to the special case of Hopf surfaces.
Subjects: Complex Variables (math.CV)
MSC classes: 32C40, 32E05, 32U10
Cite as: arXiv:1805.00584 [math.CV]
  (or arXiv:1805.00584v2 [math.CV] for this version)
  https://doi.org/10.48550/arXiv.1805.00584

Submission history

From: Samuele Mongodi [view email]
[v1] Wed, 2 May 2018 00:24:35 UTC (9 KB)
[v2] Thu, 11 Oct 2018 23:37:40 UTC (9 KB)
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