Research Focus
Geometry, topology
My research area lies in differential geometry and partial differential equations. In particular, I focus on minimal surfaces, mean curvature flow, and min-max theory. From a broader perspective, these topics arise from studying the space of all surfaces in a given 3-manifold, and the area functional defined on this space. Namely, with respective to the area functional, minimal surfaces are the critical points, mean curvature flow is the gradient flow, and min-max theory is a version of Morse theory.
Publications
- Existence of 5 minimal tori in 3-spheres of positive Ricci curvature (with Yangyang Li), arxiv:2409.09315
- Genus one singularities in mean curvature flow (with Ao Sun), arXiv:2308.05923