Directed harmonic currents near hyperbolic singularities

Viet-Anh Nguyen

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arXiv · 1411.6421

Directed harmonic currents near hyperbolic singularities

Viet-Anh Nguyen

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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.

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Viet-Anh Nguyen. 2014-11-24. Directed harmonic currents near hyperbolic singularities. https://arxiv.org/abs/1411.6421

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