Weakly complete domains in Grauert-type surfaces

  • Samuele MongodiEmail author


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.


Weakly complete Grauert-type surfaces Levi problem 

Mathematics Subject Classification

32C40 32E05 32U10 


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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Dipartimento di MatematicaPolitecnico di MilanoMilanItaly

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