Courants algébriques et courants de Liouville

• Autorzy: M. Blel , S. K. Mimouni , G. Raby
• Języki publikacji: FR EN

Abstrakty

EN

We define in ℂⁿ 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 ℂⁿ which are algebraic. Let T be a closed positive current on ℂⁿ. 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 ℂⁿ.

Kategorie tematyczne

• 32C25: Analytic subsets and submanifolds
• 12D10: Polynomials: location of zeros (algebraic theorems)
• 32C30: Integration on analytic sets and spaces, currents
• 14A20: Generalizations (algebraic spaces, stacks)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2005
• Tom: 86
• Numer: 3
• Strony: 245-271

Daty

wydano

2005

Twórcy

autor

M. Blel

• Faculté des Sciences de Monastir, Département de mathématiques, 5019 Monastir, Tunisie

autor

S. K. Mimouni

• Faculté des Sciences de Monastir, Département de mathématiques, 5019 Monastir, Tunisie

autor

G. Raby

• UMR CNRS 6086, Groupes de Lie et Géométrie, Mathématiques, Université de Poitiers, Téléport2-BP 30179, 86962 Futuroscope Chasseneuil, France

Identyfikatory

DOI

10.4064/ap86-3-4