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arXiv · 1304.3032

Directed harmonic currents for laminations on certain compact complex surfaces

Carlos Pérez-Garrandés
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Abstract

Let $\mathcal{L}$ be a Lipschitz lamination by Riemann surfaces embedded in $M$. If $M$ is a complex torus, $\mathbb{CP}^1\times\mathbb{CP}^1$ or $\mathbb{T}^1\times\mathbb{CP}^1$ and there is no directed closed current then there exists a unique directed harmonic current of mass one. Moreover if $\mathcal{L}$ is embedded in $M=\mathbb{CP}^1\times\mathbb{CP}^1$ and has no compact leaves, then there is no directed closed current. If $\mathcal{L}$ is not Lipschitz, then slightly weaker results are obtained.

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Carlos Pérez-Garrandés. 2013-04-10. Directed harmonic currents for laminations on certain compact complex surfaces. https://arxiv.org/abs/1304.3032

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