[Le problème de l'existence de courants S-plurisousharmoniques]
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.
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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@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},
publisher = {Elsevier},
volume = {353},
number = {7},
year = {2015},
doi = {10.1016/j.crma.2015.04.011},
language = {en},
url = {http://archive.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 - http://archive.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 http://archive.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, Tome 353 (2015) no. 7, pp. 605-610. doi : 10.1016/j.crma.2015.04.011. http://archive.numdam.org/articles/10.1016/j.crma.2015.04.011/
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