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.
Mongodi, S. (2019). Weakly complete domains in Grauert-type surfaces. ANNALI DI MATEMATICA PURA ED APPLICATA, 198(4), 1185-1189 [10.1007/s10231-018-0814-0].
Weakly complete domains in Grauert-type surfaces
Mongodi S.
2019
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.
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