Prolongement d'un courant positif à travers une sous-variété non Levi-plate

The purpose of this Note is to prove an extension result for positive currents satisfying one of the following conditions: either ddcT⩽0 or one of the currents dT or ddcT is of locally finite mass, across of a non-Levi-flat submanifold of class C2. We prove in the first part that a positive current of dimension p defined in the complement of the zero set of a strictly k-convex function of class C2 (k⩽p−1) and such that dT is of locally finite mass, is itself of locally finite mass. We recover a result of S. Giret in the case of a Cauchy-Riemann subvariety. To cite this article: K. Dabbek, F. Elkhadhra, C. R. Acad. Sci. Paris, Ser. I 340 (2005).