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Ahlfors regularity of Patterson-Sullivan measures of Anosov groups and applications (2401.12398v4)
Published 22 Jan 2024 in math.GR, math.DS, math.GT, math.MG, and math.SP
Abstract: For all Zarski dense Anosov subgroups of a semisimple real algebraic group, we prove that their limit sets are Ahlfors regular for intrinsic conformal premetrics. As a consequence, we obtain that a Patterson-Sullivan measure is equal to the Hausdorff measure if and only if the associated linear form is symmetric. We also discuss several applications, including analyticity of $(p,q)$-Hausdorff dimensions on the Teichm\"uller spaces, new upper bounds on the growth indicator, and $L2$-spectral properties of associated locally symmetric manifolds.
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