Abstract
Abstract Let G be a connected semisimple real algebraic group. For a Zariski dense Anosov subgroup $\Gamma <G$ with respect to a parabolic subgroup $P_\theta $ , we prove that any $\Gamma $ -Patterson–Sullivan measure charges no mass on any proper subvariety of $G/P_\theta $ . More generally, we prove that for a Zariski dense $\theta $ -transverse subgroup $\Gamma <G$ , any $(\Gamma , \psi )$ -Patterson–Sullivan measure charges no mass on any proper subvariety of $G/P_\theta $ , provided the $\psi $ -Poincaré series of $\Gamma $ diverges at its abscissa of convergence. In particular, our result also applies to relatively Anosov subgroups.
Published Version
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