Courants positifs à supports dans une bande

Let T be a positive current of bidimension (p,p) on Cn with support in a strip. If T is closed, S. Giret has proved that T admits a well defined lifting through a blow up with smooth center. The class of positive closed currents with bidimension (1,1) in the unit bidisc Δ2 and with support in a strip, plays a central role in the study of the dynamics of some holomorphic maps. In this note, we prove some estimates of the trace measure of T when ddcT⩽0, we prove in particular that if T is closed, then it is algebraic. We then prove two support theorems; the first one in the case where the degree of T is finite and the second in the case where T is positive closed and with tubular support. The latter result generalizes the case p=n−1 proved by M. Blel, S.K. Mimouni and G. Raby, which is also a generalization of the case when T is the current of integration on an hypersurface as proved by M.T. Togni. To cite this article: F. Elkhadhra, S.K. Mimouni, C. R. Acad. Sci. Paris, Ser. I 341 (2005).