Ahlfors regularity of Patterson-Sullivan measures of Anosov groups and applications
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 Teichmüller spaces, new upper bounds on the growth indicator, and $L^2$-spectral properties of associated locally symmetric manifolds.
- Publication:
-
arXiv e-prints
- Pub Date:
- January 2024
- DOI:
- 10.48550/arXiv.2401.12398
- arXiv:
- arXiv:2401.12398
- Bibcode:
- 2024arXiv240112398D
- Keywords:
-
- Mathematics - Group Theory;
- Mathematics - Dynamical Systems;
- Mathematics - Geometric Topology;
- Mathematics - Metric Geometry;
- Mathematics - Spectral Theory
- E-Print:
- New title/abstract, Introduction reorganized, 55 pages, 7 figures