I am a mathematician interested in geometric analysis. I have been working on minimal surfaces, their variational aspects, min-max theory, and their connection with mathematical models of phase transitions - particularly the Allen-Cahn equation.
When can minimal hypersurfaces be connected by mean curvature flow? (with Jingwen Chen). arXiv.org preprint: arXiv:2507.03837 [math.DG] (2025). Submitted.
Volume spectrum of fiber bundles and the widths of Berger spheres (with Jingwen Chen). arXiv.org preprint: arXiv:2505.09548 [math.DG] (2025). Submitted.
Infinitely Many Surfaces with Prescribed Mean Curvature in the Presence of a Strictly Stable Minimal Surface (with Jared Marx-Kuo). arXiv.org preprint: arXiv:2502.07098 (2025). Submitted.
Allen-Cahn equation and degenerate minimal hypersurfaces (with Jingwen Chen). arXiv.org preprint:arXiv:2402.18799 (2024). Accepted for publication in Indiana University Mathematics Journal.
Morse theory for the Allen-Cahn functional (with Jingwen Chen). Journal of Functional Analysis. 288 (9) (2025).
Mean curvature flow and low energy solutions of the parabolic Allen-Cahn equation on the three-sphere (with Jingwen Chen). The Journal of Geometric Analysis 33, 283 (2023).
Ground states of semilinear elliptic problems with applications to the Allen–Cahn equation on the sphere (with Rayssa Caju, Marco A. M. Guaraco, and Henrik Matthiesen). Calculus of Variations and Partial Differential Equations. 61, 71 (2022).
Solutions of the Allen-Cahn equation on closed manifolds in the presence of symmetry (with Rayssa Caju). Communications in Analysis and Geometry. 31 (8), 1931-1968 (2023).
The Weyl Law for the phase transition spectrum and density of limit interfaces (with Marco A. M. Guaraco). Geometric and Functional Analysis 29, 382-410 (2019).
The second inner variation of energy and the Morse index of limit interfaces. The Journal of Geometric Analysis 30, 69-85 (2020).
The Allen–Cahn equation on closed manifolds (with Marco A. M. Guaraco). Calculus of Variations and Partial Differential Equations 57 (4), 101 (2018).
The Allen-Cahn equation and variational aspects of minimal hypersurfaces. IMPA, 2018. [link]