In the late seventies, Sullivan showed that, for a convex cocompact subgroup Γ of with critical exponent , any Γ-conformal measure on of dimension δ is necessarily supported on the limit set Λ and that the conformal measure of dimension δ exists uniquely. We prove an analogue of this theorem for any Zariski dense Anosov subgroup Γ of a connected semisimple real algebraic group G of rank at most 3. We also obtain the local mixing for generalized BMS measures on including Haar measures.
Dedicated to Gopal Prasad on the occasion of his 75th birthday with respect.
"Uniqueness of Conformal Measures and Local Mixing for Anosov Groups." Michigan Math. J. 72 243 - 259, August 2022. https://doi.org/10.1307/mmj/20217222