Unique Ergodicity of Harmonic Currents on Singular Foliations of P2

2006/06/29 by John Erik Fornaess, Nessim Sibony, Fornaess, John Erik +1
Mathematics · #32S65 #57R30 #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #math.CV #math.DS #msc:32S65 #msc:57R30

paper · pdf · doi:10.48550/arxiv.math/0606744

Improved exposition

arxiv created 2009/03/11 · arxiv updated 2009/12/01

Abstract

Let F be a holomorphic foliation of P² 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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