1 citations · 2 across the 7 of their papers we have counts for
9 papers
Torus and Positive Mass stability for metrics with Ricci curvature lower bound
Edward Bryden, Zhizhang Xie
Consider a sequence of metrics on the torus whose members have uniform lower bounds on their first stable systoles and Ricci curvatures, and have a uniform upper bound on the…
Proof of the Spacetime Penrose Inequality With Suboptimal Constant in the Asymptotically Flat and Asymptotically Hyperboloidal Regimes
Brian Allen, Edward Bryden, Demetre Kazaras +1
We establish mass lower bounds of Penrose-type in the setting of -dimensional initial data sets for the Einstein equations satisfying the dominant energy condition, which are ei…
Volume Above Distance Below with Boundary II
Brian Allen, Edward Bryden
It was shown by B. Allen, R. Perales, and C. Sormani that on a closed manifold where the diameter of a sequence of Riemannian metrics is bounded, if the volume converges to the vol…
Exploring a Modification of Convergence
Brian Allen, Edward Bryden
In the work by M. C. Lee, A. Naber, and R. Neumayer a beautiful -regularity theorem is proved under small negative scalar curvature and entropy bounds. In that paper,…
On the Stability of Llarull's Theorem in Dimension Three
Brian Allen, Edward Bryden, Demetre Kazaras
Llarull's Theorem states that any Riemannian metric on the -sphere which has scalar curv{\-}ature greater than or equal to , and whose distance function is bounded below…
Stability of the positive mass theorem and torus rigidity theorems under integral curvature bounds
Brian Allen, Edward Bryden, Demetre Kazaras
Work of D. Stern and Bray-Kazaras-Khuri-Stern provide differential-geometric identities which relate the scalar curvature of Riemannian 3-manifolds to global invariants in terms of…
Sobolev Inequalities and Convergence For Riemannian Metrics and Distance Functions
Brian Allen, Edward Bryden
If one thinks of a Riemannian metric, , analogously as the gradient of the corresponding distance function, , with respect to a background Riemannian metric, , then…
Stability of the Spacetime Positive Mass Theorem in Spherical Symmetry
Edward Bryden, Marcus Khuri, Christina Sormani
The rigidity statement of the positive mass theorem asserts that an asymptotically flat initial data set for the Einstein equations with zero ADM mass, and satisfying the dominant…
Sobolev bounds and convergence of Riemannian manifolds
Brian Allen, Edward Bryden
We consider sequences of compact Riemannian manifolds with uniform Sobolev bounds on their metric tensors, and prove that their distance functions are uniformly bounded in the Höld…