Anderson-Cheeger limits of smooth Riemannian manifolds, and other Gromov-Hausdorff limits

We establish further regularity of the C alpha and H-1,H-P limits of smooth, n-dimensional Riemannian manifolds with a lower bound on Ricci tensor and injectivity radius, and an upper bound on volume, first considered in [1]. We use this extra regularity to show that such a limit is a nonbranching geodesic space, as defined in [10], and to construct a variant of a geodesic flow for such a limit. We contrast the behavior ofsome slightly more singular limits.