abstract: Let F be a holomorphic foliation by curves defined in a neighborhood of 0 in lC n(n ≥ 2) having 0 as a weakly hyperbolic singularity. Let T be a positive harmonic current directed by F which does not give mass to any of the n coordinate invariant hyperplanes {zj = 0} for 1 ≤ j ≤ n. Then we show that the Lelong number of T at 0 vanishes. Moreover, an application of this local result in the global context is given.
Keywords: singular holomorphic foliation, (weakly) hyperbolic singularity, directed positive harmonic current, directed positive ddc -closed currents, Lelong number.