Let $(M,g)$ be a complete connected $d$-dimensional Riemannian manifold equipped; let $(X_{M,g},d_g)$ denote its associated metric (length) space. Under what conditions is $(X_{M,g},d_g)$ Ahlfors $d$-regular; i.e. each $\mathcal{H}^d(B_{d_g}(x,r))\in \Theta( r^d)$?

Here $\mathcal{H}^d$ is the $d$-dimensiona Hausdorff outer measure and $B_{d_g}(x,r)$ is a metric ball about some $x \in M$ of radius $r>0$.

I guess, I'm looking for some type of Ricci-curvature constraint...but maybe my intuition is off...