Directed harmonic currents near hyperbolic singularities
Complex Variables
2016-12-16 v2
Abstract
Let \Fc be a holomorphic foliation by curves defined in a neighborhood of 0 in \C^2 having 0 as a hyperbolic singularity. Let T be a harmonic current directed by \Fc which does not give mass to any of the two separatrices. Then we show that the Lelong number of T at 0 vanishes. Next, we apply this local result to investigate the global mass-distribution for directed harmonic currents on singular holomorphic foliations living on compact complex surfaces. Finally, we apply this global result to study the recurrence phenomenon of a generic leaf.
Keywords
Cite
@article{arxiv.1411.6421,
title = {Directed harmonic currents near hyperbolic singularities},
author = {Viet-Anh Nguyen},
journal= {arXiv preprint arXiv:1411.6421},
year = {2016}
}
Comments
Ergodic Theory and Dynamical Systems (to appear), 21 pages