In previous works, Tomassini and the authors studied and classified complex surfaces admitting a real-analytic plurisubharmonic exhaustion function; let X be such a surface and D⊆ X a domain admitting a continuous plurisubharmonic exhaustion function: what can be said about the geometry of D? If the exhaustion of D is assumed to be smooth, the second author already answered this question; however, the continuous case is more difficult and requires different methods. In the present paper, we address such question by studying the local maximum sets contained in D and their interplay with the complex geometric structure of X; we conclude that, if D is not a modification of a Stein space, then it shares the same geometric features of X.

Mongodi, S., Slodkowski, Z. (2020). Domains with a continuous exhaustion in weakly complete surfaces. MATHEMATISCHE ZEITSCHRIFT, 296(3-4), 1011-1019 [10.1007/s00209-020-02466-z].

Domains with a continuous exhaustion in weakly complete surfaces

Mongodi S.
;
2020

Abstract

In previous works, Tomassini and the authors studied and classified complex surfaces admitting a real-analytic plurisubharmonic exhaustion function; let X be such a surface and D⊆ X a domain admitting a continuous plurisubharmonic exhaustion function: what can be said about the geometry of D? If the exhaustion of D is assumed to be smooth, the second author already answered this question; however, the continuous case is more difficult and requires different methods. In the present paper, we address such question by studying the local maximum sets contained in D and their interplay with the complex geometric structure of X; we conclude that, if D is not a modification of a Stein space, then it shares the same geometric features of X.
Articolo in rivista - Articolo scientifico
weakly complete, plurisubharmonic functions, approximation of plurisubharmonic functions, Grauert-type surfaces;
English
2020
296
3-4
1011
1019
reserved
Mongodi, S., Slodkowski, Z. (2020). Domains with a continuous exhaustion in weakly complete surfaces. MATHEMATISCHE ZEITSCHRIFT, 296(3-4), 1011-1019 [10.1007/s00209-020-02466-z].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/349866
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