TY - JOUR
AU - Oh, Hee
AB - 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.
TI - Dichotomy and Measures on Limit Sets of Anosov Groups
JO - International Mathematics Research Notices
DO - 10.1093/imrn/rnad188
DA - 2023-10-09
UR - https://www.deepdyve.com/lp/oxford-university-press/dichotomy-and-measures-on-limit-sets-of-anosov-groups-vJHWZwhvEy
SP - 5658
EP - 5688
VL - 2024
IS - 7
DP - DeepDyve
ER -