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.
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.
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Ahmad K. Al Abdulaali 1; Hassine El Mir 1
@article{CRMATH_2015__353_7_605_0, author = {Ahmad K. Al Abdulaali and Hassine El Mir}, title = {The existence problem of {\protect\emph{S}-plurisubharmonic} currents}, journal = {Comptes Rendus. Math\'ematique}, pages = {605--610}, publisher = {Elsevier}, volume = {353}, number = {7}, year = {2015}, doi = {10.1016/j.crma.2015.04.011}, language = {en}, }
Ahmad K. Al Abdulaali; Hassine El Mir. The existence problem of S-plurisubharmonic currents. Comptes Rendus. Mathématique, Volume 353 (2015) no. 7, pp. 605-610. doi : 10.1016/j.crma.2015.04.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.04.011/
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