Patterson-Sullivan theory for Anosov subgroups
Group Theory
2022-04-26 v4 Differential Geometry
Abstract
We extend several notions and results from the classical Patterson-Sullivan theory to the setting of Anosov subgroups of higher rank semisimple Lie groups, working primarily with invariant Finsler metrics on associated symmetric spaces. In particular, we prove the equality between the Hausdorff dimensions of flag limit sets, computed with respect to a suitable Gromov (pre-)metric on the flag manifold, and the Finsler critical exponents of Anosov subgroups.
Keywords
Cite
@article{arxiv.1904.10196,
title = {Patterson-Sullivan theory for Anosov subgroups},
author = {Subhadip Dey and Michael Kapovich},
journal= {arXiv preprint arXiv:1904.10196},
year = {2022}
}
Comments
Final version: Main notations were revised to reflect the dependence with the choice of $\bar\theta$. Section 10 was expanded, and two new appendices were added. To appear in the Transactions of the American Mathematical Society