Research

RESEARCH INTERESTS:

• Geometric analysis and PDE

• Convergence of Riemannian manifolds and Spacetimes

• Geometric stability of rigidity theorems  

• Applications to general relativity

Preprints:

1. Exploring a Modification of $d_p$ Convergence, B. Allen and E. Bryden, arXiv:2311.13450 [math.DG] November 22, 2023 (Under Review) (arxiv)

2. On the Stability of Llarull's Theorem in Dimension Three, B. Allen, E. Bryden, and D. Kazaras, arXiv:2305.18567 [math.DG] May 31, 2023 (Under review) (arxiv)

3. Stability of the Positive Mass and Torus Rigidity Theorems under Integral Curvature Bounds, B. Allen, E. Bryden, and D. Kazaras, arXiv:2210.04340[math.DG] October 9, 2022 (Under review) (arxiv)

4. Intrinsic Flat Stability of Manifolds with Boundary where Volume Converges and Distance is Bounded Below, B. Allen and R. Perales, arXiv:2006.13030 [math.DG] June 23, 2020 (Under review) (arxiv)

Publications:

1. From $L^p$ Bounds to Gromov-Hausdorff Convergence of Riemannian Manifolds, B. Allen, Geometriae Dedicata 218 no. 30 (2024) (arxiv) (ref)

2. Null Distance and Gromov-Hausdorff Convergence of Warped Product Spacetimes, B. Allen, General Relativity and Gravitation 55 no. 118 (2023) (arxiv) (ref)

3. Sobolev Inequalities and Convergence for Riemannian Manifolds and Distance Functions, B. Allen and E. Bryden, Annals of Global Analysis and Geometry 63 no. 28 (2023) (arxiv) (ref)

4. Volume Above Distance Below, B. Allen, R. Perales, and C. Sormani, arXiv:2003.01172 [math.MG] March 2, 2020 (To appear in the Journal of Differential Geometry) (arxiv)

5. Inverse Mean Curvature Flow and the Stability of the Positive Mass Theorem, B. Allen, Communications in Analysis and Geometry 31 no. 10 (2023) (arxiv) (ref)

6. Properties of the null distance and spacetime convergence, B. Allen and A. Burtscher, International Mathematics Research Notices 2022 no. 10 (2022) 7729-7808 (arxiv) (ref)

7. Almost Non-Negative Scalar Curvature on Riemannian Manifolds Conformal to Tori, B. Allen, Journal of Geometric Analysis 31 (2021) 11190-11213 (arxiv) (ref)

8. Relating notions of convergence in geometric analysis, B. Allen and C. Sormani, Nonlinear Analysis 200 (2020) (arxiv) (ref)

9. Contrasting various notions of convergence in geometric analysis, B. Allen and C. Sormani, Pacific Journal of Mathematics 303 no. 1 (2019) 1-46 (arxiv) (ref)

10. Sobolev stability of the PMT and RPI using IMCF, B. Allen, General Relativity and Gravitation (Editors Choice) 51 no. 5 (2019) (arxiv) (ref)

11. Sobolev bounds and convergence of Riemannian manifolds, B. Allen and E. Bryden, Nonlinear Analysis 185 (2019) 142-169 (arxiv) (ref)

12. Warped Tori with Almost Non-Negative Scalar Curvature, B. Allen, D. Parise, A. Payne, L. Vazquez and S. Wang, Geometriae Dedicata 200 no. 1 (2019) 153-171. (arxiv) (ref)

13. Stability of the Positive Mass Theorem and Riemannian Penrose Inequality for Asymptotically Hyperbolic Manifolds Foliated by Inverse Mean Curvature Flow, B. Allen, Journal of Mathematical Physics 59 no. 8 (2018). (arxiv) (ref)

14. IMCF and the Stability of the PMT and RPI Under $L^2$ Convergence, B. Allen, Annales Henri Poincare 19 no. 4 (2018) 1283-1306. (arxiv) (ref)

15. Geometry of Statistical Target Detection, W. Basener, B. Allen and K. Bretney, Journal of Applied Remote Sensing 11 (2017). (ref)