no. 3-4
Complex Analysis
Global and local definition of the Monge–Ampère operator on compact Kähler manifolds
[Définition globale et locale de lʼopérateur de Monge–Ampère sur les variétés kählériennes compactes]

Présenté par : Jean-Pierre Demailly

Hai, Le Mau1 ; Hiep, Pham Hoang1 ; Phu, Nguyen Van2
1 Department of Mathematics, Hanoi National University of Education, Viet Nam
2 Department of Mathematics, Electric Power University, Hanoi, Viet Nam
Comptes Rendus. Mathématique, Tome 350 (2012) no. 3-4, pp. 153-156.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2012.01.025
Hai, Le Mau 1 ; Hiep, Pham Hoang 1 ; Phu, Nguyen Van 2

1 Department of Mathematics, Hanoi National University of Education, Viet Nam
2 Department of Mathematics, Electric Power University, Hanoi, Viet Nam 
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Hai, Le Mau; Hiep, Pham Hoang; Phu, Nguyen Van. Global and local definition of the Monge–Ampère operator on compact Kähler manifolds. Comptes Rendus. Mathématique, Tome 350 (2012) no. 3-4, pp. 153-156. doi : 10.1016/j.crma.2012.01.025. http://www.numdam.org/articles/10.1016/j.crma.2012.01.025/

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