HARMONIC CURRENTS DIRECTED BY FOLIATIONS BY RIEMANN SURFACES

摘要

We study local positive dd(c)-closed currents directed by a foliation by Riemann surfaces near a hyperbolic singularity which have no mass on the separatrices. A theorem of Nguyen says that the Lelong number of such a current at the singular point vanishes. We prove that this property is sharp: one cannot have any better mass estimate for this current near the singularity.