I am reading a bit about Sormani-Wenger intrinsic flat distance between compact oriented Riemannian manifolds out of curiosity.
There are some settings which it can be shown that Gromov-Hausdorff convergence is equivalent to SWIF convergence, but is SWIF convergence in general a 'weaker' notion than Gromov-Hausdorff convergence? For example, if I understood rightly the notion of Gromov-Wasserstein convergence and Gromov-Wasserstein distance which exists in the literature is weaker than GH convergence.
