Publications:

1. Matthew J. Gursky, Stephen E. McKeown and Aaron J. Tyrrell, Renormalized Volume of Minimally Bounded Regions in Asymptotically Hyperbolic Einstein Spaces, Advances in Theoretical and Mathematical Physics, 2022 link.
2. Aaron J. Tyrrell, Renormalized Area for Minimal Hypersurfaces of 5D Poincaré-Einstein Spaces, Journal of Geometric Analysis, 2023, Link.
3. Jeffrey S. Case and Aaron J. Tyrrell, A Sharp Inequality for Trace-Free Matrices with Applications to Hypersurfaces, Proceedings of the AMS, 2023, Link.
4. Jeffrey S. Case, C. Robin Graham, Tzu-Mo Kuo, Aaron J. Tyrrell and Andrew Waldron, A Gauss-Bonnet Formula for the Renormalized Area of Minimal Submanifolds of Poincaré-Einstein Spaces, Communications in Mathematical Physics, 2025. Link.
5. Matthew J. Gursky, Stephen E. McKeown and Aaron J. Tyrrell, Self-dual and even Poincaré-Einstein metrics in dimension four, Journal of the Institute of Mathematics of Jussieu, 2026, Link.
6. Samuel Pérez-Ayala and Aaron J. Tyrrell, First Eigenvalue Estimates for Asymptotically Hyperbolic Manifolds and their Submanifolds, Revista Matemática Iberoamericana, 2026, Link.
7. Jeffrey S. Case, Ayush Khaitan, Yueh-Ju Lin, Aaron J. Tyrrell and Wei Yuan, Computing Renormalized Curvature Integrals on Poincaré-Einstein Manifolds, Advances in Mathematics, Volume 496, 2026, Link.

Pre-Prints:

1. Samuel Pérez-Ayala and Aaron J. Tyrrell, Holography and Cheeger Constant of Conformally Compact Asymptotically CMC Submanifolds, Submitted, Link.
2. Davide Dameno and Aaron J. Tyrrell, Topological and rigidity results for four-dimensional hypersurfaces in space forms, Submitted, Link.
3. Jeffrey S. Case, Ayush Khaitan, Yueh-Ju Lin, Aaron J. Tyrrell and Wei Yuan, Local and global conformal invariants of submanifolds, Submitted, Link.
4. Matthew J. Gursky, Khoi Nguyen and Aaron J. Tyrrell, Renormalized area of minimal surfaces in hyperbolic space, Submitted, Link.