Appears in collection : Not Only Scalar Curvature Seminar

The classical concept of capacity generalizes from Euclidean space to complete Riemannian manifolds, and even to suitable classes of metric spaces. I will discuss recent joint work with Raquel Perales and Jim Portegies on understanding capacity in local integral current spaces, describing the behavior of capacity when the background spaces converge in the pointed Sormani--Wenger intrinsic flat sense. Connections between the main results and the concept of total mass in general relativity will be discussed.