Research

My research interests are Analysis of Partial Differential Equations and Differential Geometry.     

Research statement (2022)

Research Publication:

1. The singular sets of degenerate and nonlocal elliptic equations on Poincaré-Einstein manifolds, with Y. Sire, R. Zhang, Submitted.

2. A continuous cusp closing process for negative Kähler-Einstein metrics, with Xin Fu and Hans-Joachim Hein, 

To appear at Geom. Func. Anal.

3. Asymptotics of Kähler-Einstein metrics on complex hyperbolic cusps, with X. Fu, H.-J. Hein,

Calc. Val. P.D.E., https://doi.org/10.1007/s00526-023-02613-4

4. The Loewner-Nirenberg Problem in cones, with Q. Han, W. Shen,

Accepted at J. Funct. Anal.

5. Boundary expansion for the Loewner-Nirenberg problem in domains with conic singularities, 

J. Funct. Anal. 281 (2021), no. 7, 109122. 35 (58)

6. Free-boundary regularity on the focusing problem for the $Q_k$ Curvature Flow with flat sides I,  with Ling Xiao,

J. Funct. Anal. 280 (2021), no. 2, 108792, 37 pp. 53E10

7. Asymptotic expansions of complete Kähler-Einstein metrics with finite volume  on quasi-projective manifolds, with Yalong Shi,

Sci. China Math. 65 (2022), no. 9, 1953–1974

8. Optimal regularity of constant curvature graphs in Hyperbolic space, with L. Xiao,

Calc. Var. P.D.E., 58:133 (2019)

9. Isometric embedding with nonnegative Gauss curvature under the graph setting,

Discrete Contin. Dyn. Syst. 39 (2019), no. 6, 3463–3477.

10. Asymptotics and convergence for the complex Monge-Ampere equation, with Q. Han, 

Annals of PDE, https://doi.org/10.1007/s40818-024-00171-2

11. Boundary regularity of minimal graphs in the hyperbolic space, with Q. Han,

Journal für die reine und angewandte Mathematik, https://doi.org/10.1515/crelle-2023-0040

12. The convergence of boundary expansions and the analyticity of minimal surfaces in the hyperbolic space, with Q. Han,

submitted.

13. Boundary expansions for minimal graphs in the hyperbolic space, Thesis (Ph.D.), University of Notre Dame (2016).