Soit (M,J) une variété presque complexe. Une application u :(M,J)→[−∞,+∞[ semi-continue supérieurement est dite plurisousharmonique si u∘ϕ est sousharmonique, pour toute courbe pseudo-holomorphe ϕ :(Δ,J0)→(M,J). En utilisant des techniques de régularisation des courants et des développements de Taylor dans des coordonnées locales adaptées à la structure J, on démontre qu'une application u :(M,J)→[−∞,+∞[ semi-continue supérieurement et non identiquement égale à −∞ est plurisousharmonique si et seulement si la partie de type (1,1) de
Let (M,J) be an almost complex manifold. An upper semi-continuous map u:(M,J)→[−∞,+∞[ is said to be plurisubharmonic if u∘ϕ is subharmonic for every pseudo-holomorphic curve: ϕ:(Δ,J0)→(M,J). By using regularization techniques for currents and Taylor series expansions in suitable coordinates with respect to the structure J, we prove that an upper semi-continuous map u:(M,J)→[−∞,+∞[ which is not identically equal to −∞ is plurisubharmonic if and only if the (1,1)-part of
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@article{CRMATH_2002__335_6_509_0,
author = {Haggui, Fathi},
title = {Fonctions {PSH} sur une vari\'et\'e presque complexe},
journal = {Comptes Rendus. Math\'ematique},
pages = {509--514},
publisher = {Elsevier},
volume = {335},
number = {6},
year = {2002},
doi = {10.1016/S1631-073X(02)02518-9},
language = {fr},
url = {https://www.numdam.org/articles/10.1016/S1631-073X(02)02518-9/}
}
TY - JOUR AU - Haggui, Fathi TI - Fonctions PSH sur une variété presque complexe JO - Comptes Rendus. Mathématique PY - 2002 SP - 509 EP - 514 VL - 335 IS - 6 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/S1631-073X(02)02518-9/ DO - 10.1016/S1631-073X(02)02518-9 LA - fr ID - CRMATH_2002__335_6_509_0 ER -
Haggui, Fathi. Fonctions PSH sur une variété presque complexe. Comptes Rendus. Mathématique, Tome 335 (2002) no. 6, pp. 509-514. doi : 10.1016/S1631-073X(02)02518-9. https://www.numdam.org/articles/10.1016/S1631-073X(02)02518-9/
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