Ahlfors regularity of Patterson-Sullivan measures of Anosov groups and applications

Autor:	Dey, Subhadip, Kim, Dongryul M., Oh, Hee
Rok vydání:	2024
Předmět:	Mathematics - Group Theory Mathematics - Dynamical Systems Mathematics - Geometric Topology Mathematics - Metric Geometry Mathematics - Spectral Theory
Druh dokumentu:	Working Paper
Popis:	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 $L^2$-spectral properties of associated locally symmetric manifolds. Comment: New title/abstract, Introduction reorganized, 55 pages, 7 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2401.12398 Zobrazit plný text záznamu View this record from Arxiv