On the tangent cones to plurisubharmonic currents

Abstract: In this paper, we study the existence of the tangent cone to a positive plurisubharmonic or plurisuperharmonic current with a suitable condition. Some Estimates of the growth of the Lelong functions associated to the current and to its $dd^c$ are given to ensure the existence of the blow-up of this current. A second proof for the existence of the tangent cone is derived from these estimates.