[Définition globale et locale de lʼopérateur de Monge–Ampère sur les variétés kählériennes compactes]
Le but de cet article est de donner une condition suffisante pour quʼune fonction dans le domaine global de définition de lʼopérateur Monge–Ampère nʼappartienne pas au domaine local de celui-ci dans le sens de Cegrell, lorsquʼon se place sur un espace projectif complexe de dimension n. En utilisant ce résultat, nous montrons que le théorème de sous-solution est faux pour des fonctions dans le domaine local de définition de lʼopérateur Monge–Ampère sur un tel espace projectif.
The aim of this Note is to give a sufficient condition in order for a function in the global domain of definition of the Monge–Ampère operator not to belong to the local domain of the former in the sense of Cegrell, when one looks at the n-dimensional complex projective space. Using this result, we show that the subsolution theorem is false for functions in the local domain of definition of the Monge–Ampère operator on such a projective space.
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@article{CRMATH_2012__350_3-4_153_0,
author = {Le Mau Hai and Pham Hoang Hiep and Nguyen Van Phu},
title = {Global and local definition of the {Monge{\textendash}Amp\`ere} operator on compact {K\"ahler} manifolds},
journal = {Comptes Rendus. Math\'ematique},
pages = {153--156},
publisher = {Elsevier},
volume = {350},
number = {3-4},
year = {2012},
doi = {10.1016/j.crma.2012.01.025},
language = {en},
}
TY - JOUR AU - Le Mau Hai AU - Pham Hoang Hiep AU - Nguyen Van Phu TI - Global and local definition of the Monge–Ampère operator on compact Kähler manifolds JO - Comptes Rendus. Mathématique PY - 2012 SP - 153 EP - 156 VL - 350 IS - 3-4 PB - Elsevier DO - 10.1016/j.crma.2012.01.025 LA - en ID - CRMATH_2012__350_3-4_153_0 ER -
%0 Journal Article %A Le Mau Hai %A Pham Hoang Hiep %A Nguyen Van Phu %T Global and local definition of the Monge–Ampère operator on compact Kähler manifolds %J Comptes Rendus. Mathématique %D 2012 %P 153-156 %V 350 %N 3-4 %I Elsevier %R 10.1016/j.crma.2012.01.025 %G en %F CRMATH_2012__350_3-4_153_0
Le Mau Hai; Pham Hoang Hiep; Nguyen Van Phu. Global and local definition of the Monge–Ampère operator on compact Kähler manifolds. Comptes Rendus. Mathématique, Volume 350 (2012) no. 3-4, pp. 153-156. doi : 10.1016/j.crma.2012.01.025. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.01.025/
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