Yangyang Li
Assistant Professor
Education
Ph.D. in Mathematics, Princeton University - 2017-2022
Bachelor of Science in Mathematical Sciences, Tsinghua University: Beijing - 2013-2017
Paris Visiting Program, Mathematics, École Normale Supérieure - 2017
Research Groups
Differential Geometry, Partial Differential Equations
Research Area
Differential Geometry, Partial Differential Equations, Geometric Measure Theory
Bio
Research Interests
Yangyang's research interests include differential geometry, partial differential equations, geometric measure theory, geometric flows, and geometric topology, with a specific focus on the existence and regularity theory of minimal submanifolds. In recent years, he has been working on problems related to anisotropic minimal surfaces, the construction of minimal surfaces with prescribed genus, and the analysis of singular behavior and generic regularity of minimal submanifolds.
Selected Publications
- Existence of Infinitely Many Minimal Hypersurfaces in Higher-dimensional Closed Manifolds with Generic Metrics, J. Differ. Geom. 124 (2) 381 - 395, June 2023. DOI: https://doi.org/10.4310/jdg/1686931604
- On the Existence of Minimal Hypersurfaces with Arbitrarily Large Area and Morse Index, Geom. Topol. 26 (6) 2713 - 2729, 2022. DOI: https://doi.org/10.2140/gt.2022.26.2713
- Minimal hypersurfaces for generic metrics in dimension 8 (joint with Zhihan Wang), Invent. math. 240, 1193–1303 (2025). DOI: https://doi.org/10.1007/s00222-025-01333-0
- Existence of 5 minimal tori in 3-spheres of positive Ricci curvature (joint with Adrian C. Chu), arXiv:2409.09315
- Existence and regularity of min-max anisotropic minimal hypersurfaces (joint with Guido De Philippis and Antonio De Rosa), arXiv:2409.15232
- Non-persistence of strongly isolated singularities, and geometric applications (joint with Alessandro Carlotto and Zhihan Wang), arXiv:2411.12677
Email: yli68@nd.edu
Fax: 574-631-6579
Office: 218 Hayes-Healy Center