Ahlfors regularity of Patterson–Sullivan measures of Anosov groups and applications
Abstract
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 Ahlfors regular (and hence 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 Teichmüller spaces, new upper bounds on the growth indicator, and upper L squared L 2 $L^2$ -spectral properties of associated locally symmetric manifolds.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Topological and Geometric Data Analysis
Advanced Topology and Set Theory
Publication details
- Journal / source
- Compositio Mathematica
- Publisher
- Cambridge University Press (CUP)
- Volume
- 162
- Issue
- 4
- Pages
- 743–791
- Publication date
- 1 April 2026
- Language
- EN