Unique Ergodicity of Harmonic Currents On Singular Foliations of {\mathbb{P}^2} |
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Authors: | John Erik Fornæss Nessim Sibony |
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Institution: | 1. Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109, USA 2. Université Paris-Sud 11, Bat 425. Mathématique, 91405, Orsay, France
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Abstract: | Let F{\mathcal{F}} be a holomorphic foliation of
\mathbbP2{\mathbb{P}^2} by Riemann surfaces. Assume all the singular points of F{\mathcal{F}} are hyperbolic. If F{\mathcal{F}} has no algebraic leaf, then there is a unique positive harmonic (1, 1) current T of mass one, directed by F{\mathcal{F}}. This implies strong ergodic properties for the foliation F{\mathcal{F}}. We also study the harmonic flow associated to the current T. |
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