Brian Allen

collaborators

4 papers

math.MG2019

Relating Notions of Convergence in Geometric Analysis

Brian Allen, Christina Sormani

We relate $L^{p}$ convergence of metric tensors or volume convergence to a given smooth metric to Intrinsic Flat and Gromov-Hausdorff convergence for sequences of Riemannian manifold…

math.DG2018

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…

math.DG2018

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 $M_{i}^{3}$ can be f…

math.MG2018

Contrasting Various Notions of Convergence in Geometric Analysis

Brian Allen, Christina Sormani

We explore the distinctions between $L^{p}$ convergence of metric tensors on a fixed Riemannian manifold versus Gromov-Hausdorff, uniform, and intrinsic flat convergence of the corre…