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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…
Almost non-negative scalar curvature on Riemannian manifolds conformal to tori
Brian Allen
In this article we reduce the geometric stability conjecture for the scalar torus rigidity theorem to the conformal case via the Yamabe problem. Then we are able to prove the case…
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…