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Comptes Rendus Mathématique
Volume 353, n° 7
pages 605-610 (juillet 2015)
Doi : 10.1016/j.crma.2015.04.011
Received : 23 February 2015 ;  accepted : 21 April 2015
The existence problem of S -plurisubharmonic currents
Le problème de l'existence de courants S -plurisousharmoniques

Ahmad K. Al Abdulaali , Hassine El Mir
 The Department of Mathematics, College of Science, King Faisal University, P.O. Box 380, Post Code 31982, Al-Ahsaa, Saudi Arabia 


In this paper, we prove the existence of the trivial extension of S -plurisubharmonic currents of bidimension   defined outside an obstacle A of Hausdorff measure  . Furthermore, a valid definition of the current   is achieved for every positive closed current T and plurisubharmonic function g . The above results rely on an improvement of a classical result due to Demailly on the Monge–Ampère operator with a sharp condition on the Hausdorff measure.

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Dans cette Note, nous montrons l'existence de l'extension triviale des courants S -plurisousharmoniques de bi-dimension  , définis en-dehors d'un obstacle A de mesure de Hausdorff  . De plus, nous montrons que le courant   est bien défini, pour tout courant positif fermé T et toute fonction plurisousharmonique g . Ces résultats reposent sur un relâchement de la condition de nullité d'une mesure de Hausdorff, dans un résultat classique de Demailly sur l'opérateur de Monge–Ampère.

The full text of this article is available in PDF format.

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