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August 2022 Uniqueness of Conformal Measures and Local Mixing for Anosov Groups
Sam Edwards, Minju Lee, Hee Oh
Michigan Math. J. 72: 243-259 (August 2022). DOI: 10.1307/mmj/20217222

Abstract

In the late seventies, Sullivan showed that, for a convex cocompact subgroup Γ of SO(n,1) with critical exponent δ>0, any Γ-conformal measure on Hn of dimension δ is necessarily supported on the limit set Λ and that the conformal measure of dimension δ exists uniquely. We prove an analogue of this theorem for any Zariski dense Anosov subgroup Γ of a connected semisimple real algebraic group G of rank at most 3. We also obtain the local mixing for generalized BMS measures on ΓG including Haar measures.

Dedication

Dedicated to Gopal Prasad on the occasion of his 75th birthday with respect.

Citation

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Sam Edwards. Minju Lee. Hee Oh. "Uniqueness of Conformal Measures and Local Mixing for Anosov Groups." Michigan Math. J. 72 243 - 259, August 2022. https://doi.org/10.1307/mmj/20217222

Information

Received: 24 November 2021; Revised: 25 January 2022; Published: August 2022
First available in Project Euclid: 2 August 2022

Digital Object Identifier: 10.1307/mmj/20217222

Subjects:
Primary: 22E40
Secondary: 37A17

Rights: Copyright © 2022 The University of Michigan

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Vol.72 • August 2022
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