Several results about Patterson–Sullivan measures for relatively Anosov groups

We prove that Patterson–Sullivan measures for relatively Anosov groups are exact dimensional with respect to visual metrics arising from suitable Gromov models. For relatively Morse groups, we further show that the scalar Cartan metric is Gromov hyperbolic, and hence induces a visual metric to which the exact dimensionality result applies. We also prove that the associated Manhattan manifolds are $C^1$-regular, and deduce that the growth indicator is $C^1$ and strictly concave on the interior of the limit cone. This is joint work with Eduardo Reyes.