My research focuses on geometry and partial differential equations, with particular emphasis on minimal surfaces, mean curvature flow, and the Allen-Cahn equation.
My research focuses on geometry and partial differential equations, with particular emphasis on minimal surfaces, mean curvature flow, and the Allen-Cahn equation.
Publications and preprints
9 When can minimal hypersurfaces be connected by mean curvature flow? (with Pedro Gaspar), arxiv.org/abs/2507.03837
8 Volume spectrum of fiber bundles and the widths of Berger spheres (with Pedro Gaspar), arxiv.org/abs/2505.09548
7 Allen-Cahn equation and degenerate minimal hypersurface (with Pedro Gaspar), arxiv.org/abs/2402.18799
Accepted by Indiana University Mathematics Journal
6 Mean curvature flow with multiplicity 2 convergence in manifolds (with Ao Sun), arxiv.org/abs/2402.04521
Mathematische Annalen, doi.org/10.1007/s00208-025-03147-0
5 Mean curvature flow with multiplicity 2 convergence in R3 (with Ao Sun), arxiv.org/abs/2312.17457
Accepted by Analysis & PDE
4 Morse theory for the Allen-Cahn functional (with Pedro Gaspar), arxiv.org/abs/2310.17096
Journal of Functional Analysis, doi.org/10.1016/j.jfa.2025.110876
3 Symmetric mean curvature flow on the n-sphere, arxiv.org/abs/2304.12282
Nonlinear Analysis, doi.org/10.1016/j.na.2023.113437
2 Mean Curvature Flow on the Three-Sphere. University of Chicago, 2023. Ph.D. thesis [link]
1 Mean curvature flow and low energy solutions of the parabolic Allen-Cahn equation on the three-sphere (with Pedro Gaspar), arxiv.org/abs/2107.09140
The Journal of Geometric Analysis, doi.org/10.1007/s12220-023-01347-1