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On defining functions for unbounded pseudoconvex domains

Mardi, 13 Novembre, 2012 - 16:00
Prénom de l'orateur : 
Nikolay
Nom de l'orateur : 
SHCHERBINA
Résumé : 

We introduce the notion of the kernel K(G) of an arbitrary
domain G in a complex manifold X as the set of all points where every bounded above plurisubharmonic function on G fails to be strictly plurisubharmonic. We show that for every strictly pseudoconvex domain G with smooth boundary in a complex manifold X there exists a global
defining function that is strictly plurisubharmonic precisely in the complement of K(G). We then investigate properties of the kernel. Among the other results we prove 1-pseudoconcavity of the kernel, and we show that in general the kernel does not posses any analytic structure.

Institution de l'orateur : 
Univ. Wuppertal
Thème de recherche : 
Analyse
Salle : 
04
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