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 Closed mean curvature flows with prescribed tangent flows (with Tang-Kai Lee, Ao Sun, Xinrui Zhao), arxiv.org/abs/2607.23879
8 When can minimal hypersurfaces be connected by mean curvature flow? (with Pedro Gaspar), arxiv.org/abs/2507.03837
Mathematische Annalen, doi.org/10.1007/s00208-026-03479-5
7 Volume spectrum of fiber bundles and the widths of Berger spheres (with Pedro Gaspar), arxiv.org/abs/2505.09548
6 Allen-Cahn equation and degenerate minimal hypersurface (with Pedro Gaspar), arxiv.org/abs/2402.18799
Indiana University Mathematics Journal
5 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
4 Mean curvature flow with multiplicity 2 convergence in R3 (with Ao Sun), arxiv.org/abs/2312.17457
Analysis & PDE, doi.org/10.2140/apde.2026.19.1029
3 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
2 Symmetric mean curvature flow on the n-sphere, arxiv.org/abs/2304.12282
Nonlinear Analysis, doi.org/10.1016/j.na.2023.113437
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
Ph.D. thesis : Mean Curvature Flow on the Three-Sphere. University of Chicago, 2023. [link]