• Corpus ID: 244709505

Uniqueness of conformal measures and local mixing for Anosov groups

@inproceedings{Edwards2021UniquenessOC,
  title={Uniqueness of conformal measures and local mixing for Anosov groups},
  author={Sam O. Edwards and Minju M. Lee and Hee Oh},
  year={2021}
}
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 ∂H 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 Γ\G… 
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3 Citations

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Let G be a connected semisimple real algebraic group. For a Zariski dense Anosov subgroup Γ < G, we show that a Γ-conformal measure is supported on the limit set of Γ if and only if its dimension is…
TEMPEREDNESS OF L2(Γ\G) AND POSITIVE EIGENFUNCTIONS IN HIGHER RANK
  • Mathematics
  • 2022
Let G = SO◦(n, 1)×SO◦(n, 1) and X = H×H for n ≥ 2. For a pair (π1, π2) of non-elementary convex cocompact representations of a finitely generated group Σ into SO◦(n, 1), let Γ = (π1 × π2)(Σ).…
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