Courants algébriques et courants de Liouville

M. Blel¹ ; S. K. Mimouni¹ ; G. Raby²

¹ Faculté des Sciences de Monastir Département de mathématiques 5019 Monastir, Tunisie
² UMR CNRS 6086 Groupes de Lie et Géométrie Mathématiques Université de Poitiers Téléport2-BP 30179 86962 Futuroscope Chasseneuil, France

Annales Polonici Mathematici, Tome 86 (2005) no. 3, pp. 245-271

Résumé

We define in $\mathbb C^n$ the concepts of algebraic currents and Liouville currents, thus extending the concepts of algebraic complex subsets and Liouville subsets. After having shown that every algebraic current is Liouville, we characterize those positive closed currents on $\mathbb C^n$ which are algebraic. Let $T$ be a closed positive current on $\mathbb C^n$. We give sufficient conditions, relating to the growth of the projective mass of $T$, so that $T$ is Liouville. These results generalize those previously obtained by N. Sibony and P. M. Wong, and K. Takegoshi in the geometrical case, i.e. when $T=[X]$ is the current of integration on an analytical complex subset of $\mathbb C^n$.

Détail

DOI : 10.4064/ap86-3-4

Mots-clés : define mathbb concepts algebraic currents liouville currents extending concepts algebraic complex subsets liouville subsets after having shown every algebraic current liouville characterize those positive closed currents mathbb which algebraic closed positive current mathbb sufficient conditions relating growth projective mass liouville these results generalize those previously obtained sibony wong takegoshi geometrical current integration analytical complex subset mathbb