Abstract: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 Nguyên 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.

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中文翻译：

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由 Riemann 曲面的叶面引导的谐波电流

摘要：我们研究了双曲奇点附近没有质量的双曲奇点附近由叶理引导的局部正 $dd^{c}$-闭合电流。Nguyên 的一个定理说这种电流在奇点处的 Lelong 数消失了。我们证明了这一特性是尖锐的：对于奇点附近的电流，没有更好的质量估计。

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