6 papers
Existence of uniform Temple charts and applications to null distance
Benjamin Meco, Anna Sakovich, Christina Sormani
In this paper, we prove that Temple's cylindrical future null coordinate charts can be constructed uniformly and we estimate the gradients of their optical functions. We then apply…
Geometric Stability of the Schoen-Yau Zero Mass Theorem
Christina Sormani
In 1979, Schoen and Yau proved their famous Positive Mass Theorem which is a combination of a comparison theorem: {\em a three dimensional asymptotically flat Riemannian manifold w…
Gromov's Compactness Theorem for the Intrinsic Timed-Hausdorff Distance
Mauricio Che, Raquel Perales, Christina Sormani
The intrinsic timed-Hausdorff distance between timed-metric spaces, first introduced by Sakovich--Sormani, yields a weak notion of convergence for space-times. In this paper we pro…
Geometric Convergence to an Extreme Limit Space with nonnegative scalar curvature
Christina Sormani, Wenchuan Tian, Wai-Ho Yeung
In 2014, Gromov conjectured that sequences of manifolds with nonnegative scalar curvature should have subsequences which converge in some geometric sense to limit spaces with some…
Introducing Various Notions of Distances between Space-Times
Anna Sakovich, Christina Sormani
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 Andersson-H…
Monotone Sequences of Metric Spaces with Compact Limits
R. Perales, C. Sormani
In this paper, we consider a fixed metric space (possibly an oriented Riemannian manifold with boundary) with an increasing sequence of distance functions and a uniform upper bound…