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.
Accepted:
Published online:
Al Abdulaali, Ahmad K. 1 ; El Mir, Hassine 1
@article{CRMATH_2015__353_7_605_0,
author = {Al Abdulaali, Ahmad K. and El Mir, Hassine},
title = {The existence problem of {\protect\emph{S}-plurisubharmonic} currents},
journal = {Comptes Rendus. Math\'ematique},
pages = {605--610},
year = {2015},
publisher = {Elsevier},
volume = {353},
number = {7},
doi = {10.1016/j.crma.2015.04.011},
language = {en},
url = {https://numdam.org/articles/10.1016/j.crma.2015.04.011/}
}
TY - JOUR AU - Al Abdulaali, Ahmad K. AU - El Mir, Hassine TI - The existence problem of S-plurisubharmonic currents JO - Comptes Rendus. Mathématique PY - 2015 SP - 605 EP - 610 VL - 353 IS - 7 PB - Elsevier UR - https://numdam.org/articles/10.1016/j.crma.2015.04.011/ DO - 10.1016/j.crma.2015.04.011 LA - en ID - CRMATH_2015__353_7_605_0 ER -
%0 Journal Article %A Al Abdulaali, Ahmad K. %A El Mir, Hassine %T The existence problem of S-plurisubharmonic currents %J Comptes Rendus. Mathématique %D 2015 %P 605-610 %V 353 %N 7 %I Elsevier %U https://numdam.org/articles/10.1016/j.crma.2015.04.011/ %R 10.1016/j.crma.2015.04.011 %G en %F CRMATH_2015__353_7_605_0
Al Abdulaali, Ahmad K.; El Mir, Hassine. 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
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