no. 3
Complex analysis
Logarithmic potentials on Pn
[Potentiels logarithmiques sur Pn]

Présenté par : Jean-Pierre Demailly

Assila, Fatima Zahra1
1 Université Ibn Tofail, avenue de l'Université, Kénitra, Maroc
Comptes Rendus. Mathématique, Tome 356 (2018) no. 3, pp. 283-287.

On étudie le potentiel logarithmique projectif Gμ d'une mesure de probabilité μ sur l'espace projectif complexe Pn. On établit que l'image de l'opérateur μ⟶Gμ est contenue dans le domaine de définition (local) de l'opérateur de Monge–Ampère complexe agissant sur les fonctions quasi-plurisousharmoniques dans Pn par rapport à la métrique de Fubini–Study. Si μ n'a pas d'atomes, on montre que la mesure de Monge–Ampère complexe du potentiel logarithmique de μ est absolument continue par rapport à la forme volume de Fubini–Study de Pn.

We study the projective logarithmic potential Gμ of a probability measure μ on the complex projective space Pn. We prove that the range of the operator μ⟶Gμ is contained in the (local) domain of definition of the complex Monge–Ampère operator acting on the class of quasi-plurisubharmonic functions on Pn with respect to the Fubini–Study metric. Moreover, when the measure μ has no atom, we show that the complex Monge–Ampère measure of its logarithmic potential is an absolutely continuous measure with respect to the Fubini–Study volume form on Pn.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2018.02.004
Assila, Fatima Zahra 1

1 Université Ibn Tofail, avenue de l'Université, Kénitra, Maroc 
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Assila, Fatima Zahra. Logarithmic potentials on $ {\mathbb{P}}^{n}$. Comptes Rendus. Mathématique, Tome 356 (2018) no. 3, pp. 283-287. doi : 10.1016/j.crma.2018.02.004. http://archive.numdam.org/articles/10.1016/j.crma.2018.02.004/

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