Abstract Inspired by the Gromov-Hausdorff distance, we define a new notion called the
intrinsic flat distance between oriented m dimensional Riemannian manifolds with boundary …

We study the stability of the positive mass theorem using the intrinsic flat distance. In
particular we consider the class of complete asymptotically flat rotationally symmetric …

Gromov proved that sequences of Riemannian manifolds with nonnegative sectional
curvature have subsequences which converge in the Gromov-Hausdor sense to Alexandrov …

We relate L p convergence of metric tensors or volume convergence to a given smooth
metric to intrinsic flat and Gromov–Hausdorff convergence for sequences of Riemannian …

We look for minimal conditions on a two-dimensional metric surface X of locally finite
Hausdorff 2-measure under which X admits an (almost) parametrization with good geometric …

We consider sequences of metrics, $ g_j $, on a Riemannian manifold, $ M $, which
converge smoothly on compact sets away from a singular set $ S\subset M $, to a metric …

Given a compact, connected, and oriented manifold with boundary $ M $ and a sequence of
smooth Riemannian metrics defined on it, $ g_j $, we prove volume preserving intrinsic flat …

We study metric spaces homeomorphic to a closed oriented manifold from both geometric
and analytic perspectives. We show that such spaces (which are sometimes called metric …

We consider rotationally symmetric spaces with low regularity, which we regard as integral
currents spaces or manifolds with Sobolev regularity that are assumed to have nonnegative …

The rigidity of the Riemannian positive mass theorem for asymptotically hyperbolic
manifolds states that the total mass of such a manifold is zero if and only if the manifold is …