Existence of tangent cones to plurisubharmonic currents.

Given an integer 1 ≤ p ≤ n − 1, we consider a plurisubharmonic positive currentTof bidimension (p, p) on an open subset of ℂncontaining the origin. The tangent cone toTat the origin, if it exists, is the weak limit of dilations ofTby homotheties. Even when the tangent cone fails to exist, every weak limit at 0 of a subsequence of dilations ofTis a positive, plurisubharmonic conical current on ℂnwith the same Lelong number at the origin asT. We give a sufficient condition, in terms of estimates of the mass of the trace measure, for the existence of the tangent cone. [ABSTRACT FROM AUTHOR]