4 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…
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,…
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…