The rigidity of the Positive Mass Theorem states that the only complete asymptotically flat
manifold of nonnegative scalar curvature and zero mass is Euclidean space. We study the …

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

Abstract By works of Schoen–Yau and Gromov–Lawson any Riemannian manifold with
nonnegative scalar curvature and diffeomorphic to a torus is isometric to a flat torus. Gromov …

One of the most powerful theorems in metric geometry is the Arzela–Ascoli Theorem which
provides a continuous limit for sequences of equicontinuous functions between two compact …

The paper is devoted to geometrical investigation of Gromov–Hausdorff distance on the
classes of all metric spaces and of all bounded metric spaces. The main attention is paid to …

This is an intuitive survey of extrinsic and intrinsic notions of convergence of manifolds
complete with pictures of key examples and a discussion of the properties associated with …

We introduce the notion of causally-null-compactifiable space-times which can be
canonically converted into a compact timed-metric-spaces using the cosmological time of …

In this paper, the continuity of the set-valued map,, is proved where is the closed ball of
radius in the space centered at the origin, is a finite and positive measure space, and is a …

One of the most powerful theorems in metric geometry is the Arzela-Ascoli Theorem which
provides a continuous limit for sequences of equicontinuous functions between two compact …

The author defines and analyzes the 1/k length spectra, L1/k (M), whose union, over all k∈
N is the classical length spectrum. These new length spectra are shown to converge in the …