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A characterization of harmonic measures on laminations by hyperbolic Riemann surfaces

Yuri Bakhtin; Matilde Martánez — 2008

Annales de l'I.H.P. Probabilités et statistiques

$ℒ$ denotes a (compact, nonsingular) lamination by hyperbolic Riemann surfaces. We prove that a probability measure on $ℒ$ is harmonic if and only if it is the projection of a measure on the unit tangent bundle $T^{1} ℒ$ of $ℒ$ which is invariant under both the geodesic and the horocycle flows.

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