25 citations · 102 across the 18 of their papers we have counts for
5 papers · 1 filter
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…
Sobolev stability of the PMT and RPI using IMCF
Brian Allen
We study the Sobolev stability of the Positive Mass Theorem (PMT) and the Riemannian Penrose Inequality (RPI) in the case where a region of a sequence of manifolds can be f…
Inverse Mean Curvature Flow and the Stability of the Positive Mass Theorem
Brian Allen
We study the stability of the Positive Mass Theorem (PMT) in the case where a sequence of regions of manifolds with positive scalar curvature are foliated by a…
Warped Tori with Almost Non-Negative Scalar Curvature
Brian Allen, Lisandra Hernandez-Vazquez, Davide Parise +2
For sequences of warped product metrics on a -torus satisfying the scalar curvature bound , uniform upper volume and diameter bounds, and a uniform lower…
Contrasting Various Notions of Convergence in Geometric Analysis
Brian Allen, Christina Sormani
We explore the distinctions between convergence of metric tensors on a fixed Riemannian manifold versus Gromov-Hausdorff, uniform, and intrinsic flat convergence of the corre…