Hi there! My name is Ruijia Zhang. I am currently an Assistant Professor at the School of Mathematics, Sun Yat-sen University, Guangzhou, starting from August 2025.

I completed my postdoctoral research at Peking University in July 2025, under the guidance of Professor Yuguang Shi. Before that, in 2023, I earned my Ph.D. from Tsinghua University under the supervision of Professor Haizhong Li. My research interests lie in differential geometry and partial differential equations, with a recent focus on geometric flows and their applications. Please feel free to contact me if you are interested in my research.

News

• [03/2026] Our new preprint Pogorelov interior estimates for general sum-type Hessian equations is out! This is a joint work with Professor Weisong Dong and Sirui Xu.
• [08/2025] My paper $C^2$ estimates for $k$-Hessian equations and a rigidity theorem has been accepted for publication and published in Advances in Mathematics.
• [08/2025] I have joined the School of Mathematics, Sun Yat-sen University as an Assistant Professor.
• [07/2025] I completed my postdoctoral research at Peking University, under the guidance of Professor Yuguang Shi.
• [01/2023] I earned my Ph.D. from Tsinghua University.

Publication

• $C^2$ estimates for $k$-Hessian equations and a rigidity theorem, Advances in Mathematics, Volume 480, Part A, 2025.
• Asymptotic convergence for a class of anisotropic curvature flows (with Haizhong Li and Botong Xu), The Journal of Functional Analysis, 2022, 282(12), Paper No. 109460, 34 pp.
• A flow approach to the prescribed Gaussian curvature problem in $\mathbb{H}^{n+1}$ (with Haizhong Li), Advances in Calculus of Variations, 2024, 17(3), 521–543.
• A curvature flow approach to $L^p$ Christoffel-Minkowski problem for $1<p<k+1$, Results in Mathematics, 2024, 79(2), Paper No. 53, 22 pp.
• Curvature estimates for semi-convex solutions of asymptotic Plateau problem in $\mathbb{H}^{n+1}$ (with Han Hong), arXiv:2408.09428.
• Pogorelov interior estimates for general sum-type Hessian equations, (with Weisong Dong and Sirui Xu), arXiv:2603.15345.

Education&Employment

Assistant Professor in the School of Mathematics, Sun Yat-sen University, 2025-now
Postdoctor in Key Laboratory of Mathematics and Its Applications, Peking University, 2023-2025 (under the mentorship of Professor Yuguang Shi)
PhD in Department of Mathematical Sciences, Tsinghua University, 2017-2022 (under the supervision of Professor Haizhong Li)
BSc in Mathematics, Sichuan University, 2013-2017