English

Harmonic currents directed by foliations by Riemann surfaces

Dynamical Systems 2020-10-09 v1 Complex Variables

Abstract

We study local positive harmonic currents directed by a foliation by Riemann surfaces near a hyperbolic singularity which have no mass on the separatrices. A theorem of Nguy\^en 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.

Cite

@article{arxiv.2010.03796,
  title  = {Harmonic currents directed by foliations by Riemann surfaces},
  author = {Tien-Cuong Dinh and Hao Wu},
  journal= {arXiv preprint arXiv:2010.03796},
  year   = {2020}
}
R2 v1 2026-06-23T19:09:34.677Z