The intrinsic flat distance between compact oriented Riemannian manifolds with boundary was first introduced in joint work with Stefan Wenger building upon Ambrosio-Kirchheim's notion of currents on metric spaces and imitating Federer-Flemming's flat distance between submanifolds in Euclidean space. The limit spaces obtained under intrinsic flat convergence are countably H^m rectifiable metric spaces of the same dimension as the sequence. If the sequence of manifolds has a Gromov- Hausdorff limit, then a subsequence has an intrinsic flat limit which is a subset of the Gromov-Hausdorff limit, possibly the zero space. In joint work with Wenger, we showed the two kinds of limits agree when the Ricci curvature is nonnegative.

More recently, in joint work with doctoral student, Sajjad Lakzian, we have applied and extended this work to study manifolds which converge smoothly away from singular sets. In his further solo work, Sajjad Lakzian has proven that when the sequence of manifolds has Ricci curvature bounded below by a negative constant and converges away from a singular set of codimension one Hausdorff measure 0 with sufficient control on diameters and volumes near the singular set then the Gromov-Hausdorff limit is the metric completion of the smooth limit away from the singular set and the Intrinsic Flat Limit is everything except points of lower density. Lakzian has also proven the Angenent-Caputo-Knopf Ricci flow through a singularity is continuous with respect to the intrinsic flat distance.