We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Dichotomy and Measures on Limit Sets of Anosov Groups.
- Authors
Lee, Minju; Oh, Hee
- Abstract
Let |$G$| be a connected semisimple real algebraic group. For a Zariski dense Anosov subgroup |$\Gamma <G$| , we show that a |$\Gamma $| -conformal measure is supported on the limit set of |$\Gamma $| if and only if its dimension is |$\Gamma $| -critical. This implies the uniqueness of a |$\Gamma $| -conformal measure for each critical dimension, answering the question posed in our earlier paper with Edwards [ 13 ]. We obtain this by proving a higher rank analogue of the Hopf–Tsuji–Sullivan dichotomy for the maximal diagonal action. Other applications include an analogue of the Ahlfors measure conjecture for Anosov subgroups.
- Subjects
LOGICAL prediction; MEASUREMENT
- Publication
IMRN: International Mathematics Research Notices, 2024, Vol 2024, Issue 7, p5658
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnad188