Croissance de la trace d'un courant positif fermé sur les plans complexes de Cn

Let T be a closed positive current of dimension p in Cn and H an analytic subvariety of Cn of dimension n−q(1⩽q⩽p). We denote by 〈T,H〉 the slice of T in H if it exists. We consider the functions on ]0,+∞[ defined by nT(r)=r−2p∫|z|⩽rT∧βp and nT(H,r)=r−2(p−q)∫|z|⩽r〈T,H〉∧βp−q. The aim of this paper is to establish relationship between the growth of these functions. We prove results generalizing those of L. Gruman in [Séminaire Lelong-Skoda 1981-1983, Lecture Notes in Math., vol. 1028, Springer-Verlag, Berlin, 1983, pp. 125-162] and B. Molzan, B. Shiffman and N. Sibony in [Math. Ann. 257 (1981) 43].