Courants algébriques et courants de Liouville

Tom 86 / 2005

M. Blel, S. K. Mimouni, G. Raby Annales Polonici Mathematici 86 (2005), 245-271 MSC: 32C25, 32C30, 12D10, 14A20. DOI: 10.4064/ap86-3-4

Streszczenie

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 $\mathbb C^n$.

Autorzy

  • M. BlelFaculté des Sciences de Monastir
    Département de mathématiques
    5019 Monastir, Tunisie
    e-mail
    e-mail
  • S. K. MimouniFaculté des Sciences de Monastir
    Département de mathématiques
    5019 Monastir, Tunisie
    e-mail
  • G. RabyUMR CNRS 6086
    Groupes de Lie et Géométrie
    Mathématiques
    Université de Poitiers
    Téléport2-BP 30179
    86962 Futuroscope Chasseneuil, France
    e-mail

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