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Unique Ergodicity of Harmonic Currents on Singular Foliations of P2

John Erik Fornaess·Nessim Sibony
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Abstract

Let F be a holomorphic foliation of P^2 by Riemann surfaces. Assume all the singular points of F are hyperbolic. If F has no algebraic leaf, then there is a unique positive harmonic $(1,1)$ current $T$ of mass one, directed by F. This implies strong ergodic properties for the foliation. We also study the harmonic flow associated to the current $T.$

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John Erik Fornaess, Nessim Sibony. 2009-03-11. Unique Ergodicity of Harmonic Currents on Singular Foliations of P2. https://arxiv.org/abs/math/0606744

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