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}
}