4 papers
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…
On the Scalar Curvature Compactness Conjecture in the Conformal Case
Brian Allen, Wenchuan Tian, Changliang Wang
Is a sequence of Riemannian manifolds with positive scalar curvature, satisfying some conditions to keep the sequence reasonable, compact? What topology should one use for the conv…