My research interests are mainly in partial differential equations. More specifically, my current research focuses on the Monge-Ampère equations and the linearized Monge-Ampère equations.
(with Guoqing Cui, Nam Q. Le, Ling Wang, and Bin Zhou) Global Hölder estimates for linearized Monge-Ampère equations in divergence form with applications to dual semigeostrophic equations and periodic homogenization, arXiv:2610.02071. pdf
Uniqueness and sharp boundary estimates for degenerate Monge-Ampère equations with singular measures, arXiv:2609.27341. pdf
Triangles minimize the Monge-Ampère eigenvalue among planar bounded convex domains of a given area, arXiv:2609.15563. pdf
(with Nam Q. Le) A Green’s function approach to linearized Monge–Ampère equations in divergence form and application to singular Abreu type equations, J. Lond. Math. Soc. (2). 114 (2026), no. 1, Paper No. e70644 (37 pages). pdf