• 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… 
3 Citations
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  • 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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References

SHOWING 1-10 OF 14 REFERENCES
Local mixing of one-parameter diagonal flows on Anosov homogeneous spaces
Let G be a connected semisimple real algebraic group and Γ < G be an Anosov subgroup with respect to a minimal parabolic subgroup. We prove local mixing of the one-parameter diagonal flow {exp(tv) :
THE HOPF-TSUJI-SULLIVAN DICHOTOMY FOR ANOSOV GROUPS IN LOW AND HIGH RANK
Let G be a connected semisimple real algebraic group. We establish an analogue of the Hopf-Tsuji-Sullivan dichotomy for any regular Zariski dense discrete subgroup of G. We deduce the following
Anosov representations: domains of discontinuity and applications
The notion of Anosov representations has been introduced by Labourie in his study of the Hitchin component for SL(n,R). Subsequently, Anosov representations have been studied mainly for surface
Propriétés Asymptotiques des Groupes Linéaires
Abstract. Let G be a reductive linear real Lie group and $\Gamma$ be a Zariski dense subgroup. We study asymptotic properties of $\Gamma$ through the set of logarithms of the radial components of
Invariant measures for horospherical actions and Anosov groups
Let $\Gamma$ be an Anosov subgroup of a connected semisimple real linear Lie group $G$. For a maximal horospherical subgroup $N$ of $G$, we show that the space of all non-trivial $NM$-invariant
Anosov groups: local mixing, counting, and equidistribution
For a Zariski dense Anosov subgroup $\Gamma$ of a semisimple real Lie group $G$, we describe the asymptotic behavior of matrix coefficients $\Phi(g)=\langle g f_1, f_2\rangle$ in
Anosov flows, surface groups and curves in projective space
Note that in [10], W. Goldman gives a complete description of these connected components in the case of finite covers of PSL(2,R). In the case of PSL(2,R), two homeomorphic components, called
Mesures de Patterson—Sullivan en rang supérieur
Abstract. Let G be a semisimple Lie group with finite center and $ \Gamma $ a discrete Zariski dense subgroup of G. We use here the indicator of growth of $ \Gamma $, introduced in [Q3], to build
The density at infinity of a discrete group of hyperbolic motions
© Publications mathématiques de l’I.H.É.S., 1979, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » ( http://www.
Divergence exponentielle des sous-groupes discrets en rang supérieur
Abstract. Soient G un groupe de Lie semi-simple, réel, connexe et de centre fini, $ \mathfrak a $ un sous-espace de Cartan de l‚algèbre de Lie de G et $ \mathfrak a^{+} \subset \mathfrak a $ une
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