My primary research interests are nonlinear Partial Differential Equations and their applications.

My articles on arXiv

My Google Scholar Profile 

Preprints

1. Liouville theorem with boundary conditions from Chern--Gauss--Bonnet formula (joint with Y.Y. Li and Z. Li), arXiv:2410.16384 [math.AP].

2. On the fully nonlinear Yamabe problem with constant boundary mean curvature. I (joint with Y.Y. Li and Z. Li), arXiv:2410.09683 [math.AP].

3. Liouville theorems for conformally invariant fully nonlinear equations. I (joint with Y.Y. Li and Z. Li),  arXiv:2311.07542 [math.AP]. 

Publications

1. On the Fully Nonlinear Yamabe Problem, Ph.D. Dissertation, Rutgers, The State University of New Jersey, 2025.

Invited Talks & Academic Visits

1. TBD (Online Talk), Geometry and Topology Seminar, McMaster University, Canada, Nov 20, 2025.

2. TBD, University of California - San Diego, USA, Nov 13, 2025. 

3. Optimal Liouville theorems for second order conformally invariant equations, 45-minute talk, Special Session on "Nonlinear Elliptic PDEs and Geometry”, AMS Western Sectional Meeting on 2025 Fall, University of Denver, Denver, USA, Aug 23-24, 2025.

4. Optimal Liouville theorems for second order conformally invariant equations, Workshop on Topics in Differential Geometry, Brown University, Providence, USA, Jun 11-13, 2025.

5. Some recent developments on the fully nonlinear Yamabe problems, Analysis Seminar, Northwestern University, Evanston, USA, Apr 7, 2025.

6. Some recent developments on the fully nonlinear Yamabe problems, Analysis & PDE Seminar, Johns Hopkins University, Baltimore, USA, Feb 10, 2025.

7. Liouville theorems for second order conformally invariant equations and their applications, Geometry and Topology Seminar, University of Wisconsin--Madison, USA, Oct 25, 2024. 

8. Liouville theorems for conformally invariant fully nonlinear equations, Special session on "Regularity of Nonlinear Equations and Free Boundary Problems", AMS Eastern Sectional Meeting on Fall 2024, University at Albany--State University of New York, Albany, USA, Oct 19-20, 2024.

9. Maximum principle for singular solutions of nonlinear elliptic equations and its applications, A Mini Course on PDEs, Beijing Normal University, Beijing, China, June 24-26, 2024.

10. Visiting Scholar, City University of Hong Kong, Hong Kong, May 7-17, 2024.

11. Optimal Liouville theorems for fully nonlinear conformally invariant equations, Special Session on "Dynamics and Regularity of PDEs", Joint Mathematics Meetings (JMM) 2024, San Francisco, USA, Jan 5, 2024.

12. Conformally invariant elliptic equations: Liouville and Yamabe, Geometric Analysis Seminar, Xiamen University, Xiamen, China, Jun 1, 2023.

13. On the Liouville theorems and viscosity solutions, A Mini Course on PDEs, Beijing Normal University, Beijing, China, May 10, 2023.  

Services

1. Co-organizer, AMS Special Session on "Recent Advances in Elliptic PDEs and Their Applications", Joint Mathematics Meetings (JMM) 2026, Washington, D.C., Jan 6, 2026.