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December 2008 A characterization of harmonic measures on laminations by hyperbolic Riemann surfaces
Yuri Bakhtin, Matilde Martínez
Ann. Inst. H. Poincaré Probab. Statist. 44(6): 1078-1089 (December 2008). DOI: 10.1214/07-AIHP147

Abstract

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

$\mathcal{L}$ denote une lamination (compacte, nonsingulière) par surfaces de Riemann hyperboliques. On montre qu’ une mesure sur $\mathcal{L}$ est harmonique si et seulement si elle est la projection d’une mesure sur le fibré tangent unitaire $T^{1}\mathcal{L}$ qui est invariante sous les flots géodesique et horocyclique.

Citation

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Yuri Bakhtin. Matilde Martínez. "A characterization of harmonic measures on laminations by hyperbolic Riemann surfaces." Ann. Inst. H. Poincaré Probab. Statist. 44 (6) 1078 - 1089, December 2008. https://doi.org/10.1214/07-AIHP147

Information

Published: December 2008
First available in Project Euclid: 21 November 2008

zbMATH: 1189.37033
MathSciNet: MR2469335
Digital Object Identifier: 10.1214/07-AIHP147

Subjects:
Primary: 37C12, 37D40, 58J65

Rights: Copyright © 2008 Institut Henri Poincaré

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Vol.44 • No. 6 • December 2008
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