Research

My updated arxiv pre-prints can be found at the following link: Pre-prints.

Publications:

  1. Matthew J. Gursky, Stephen E. McKeown, Aaron J. Tyrrell: Renormalized volume of minimally bounded regions in asymptotically hyperbolic Einstein spaces, Advances in Theoretical and Mathematical Physics, volume 26, 2022, Journal link
  2. Aaron J. Tyrrell: Renormalized Area for Minimal Hypersurfaces of 5D Poincaré-Einstein Spaces, Journal of Geometric Analysis, volume 33, 2023, Journal link.
  3. Jeffrey S. Case, Aaron J. Tyrrell: A Sharp Inequality for Trace-Free Matrices with Applications to Hypersurfaces, Proceedings of the AMS, volume 152, 2023, Journal link.
  4. Jeffrey S. Case, C. Robin Graham, Tzu-Mo Kuo, Aaron J. Tyrrell, Andrew Waldron: A Gauss-Bonnet formula for the renormalized area of minimal submanifolds of Poincaré-Einstein manifolds, Communications in Mathematical Physics, Volume 406, Article number 53, 2025 Journal link.

Pre-Prints:

  1. Samuel Pérez-Ayala, Aaron J. Tyrrell: First Eigenvalue Estimates for Asymptotically Hyperbolic Manifolds and their Submanifolds, arxiv:2404.07365.
  2. Jeffrey S. Case, Ayush Khaitan, Yueh-Ju Lin, Aaron J. Tyrrell, Wei Yuan: Computing renormalized curvature integrals on Poincaré-Einstein manifolds, arxiv:2404.11319.
  3. Matthew J. Gursky, Stephen E. McKeown and Aaron J. Tyrrell, Self-dual and even Poincaré-Einstein metrics in dimension four, arxiv:2407.08851.
  4.  Samuel Pérez-Ayala and Aaron J. Tyrrell, Holography and Cheeger Constant of Conformally Compact Asymptotically CMC Submanifolds, arxiv:2503.12703.

Recorded Talks:

Geometric Analysis, Past, Present and Future: Part 1, Part 2.