Abstract
Let \({\mathcal{F}}\) be a holomorphic foliation of \({\mathbb{P}^2}\) by Riemann surfaces. Assume all the singular points of \({\mathcal{F}}\) are hyperbolic. If \({\mathcal{F}}\) has no algebraic leaf, then there is a unique positive harmonic (1, 1) current T of mass one, directed by \({\mathcal{F}}\). This implies strong ergodic properties for the foliation \({\mathcal{F}}\). We also study the harmonic flow associated to the current T.
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Fornæss, J.E., Sibony, N. Unique Ergodicity of Harmonic Currents On Singular Foliations of \({\mathbb{P}^2}\) . Geom. Funct. Anal. 19, 1334–1377 (2010). https://doi.org/10.1007/s00039-009-0043-1
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DOI: https://doi.org/10.1007/s00039-009-0043-1