Weakly complete domains in Grauert type surfaces

2018/05/02 by Samuele Mongodi, Mongodi, Samuele
Mathematics · #32C40 #32E05 #32U10 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:32C40 #msc:32E05 #msc:32U10

paper · pdf · doi:10.48550/arxiv.1805.00584

arxiv created 2018/10/11 · arxiv updated 2018/10/15

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.

Related

• Weakly complete complex surfaces
• Some properties of Grauert type surfaces
• Domains with a continuous exhaustion in weakly complete surfaces
• Bounded domains which are universal for minimal surfaces
• Plurisubharmonic exhaustion functions and almost complex Stein structures