Differential geometry and geometric analysis.  Recent  research projects include geometric flows of G2 structures, geometry flows of  hypersurfaces, and their applications in geometry and topology.

Full list of publications can be found in MathSciNet

25. Volume preserving flows in anisotropic geometries (with Ben Andrews, Yitao Lei, Changwei Xiong).   Calc. Var. Partial Differential Equations 64 (2025), no. 9, Paper No. 287, 49 pp. 

24. Anisotropic Gauss curvature flow of complete non-compact graphs (with Shujing Pan), J. Geom. Phys. 218 (2025), Paper No. 105648, 20 pp.

23. On Natário's Minkowski-type inequality in the hyperbolic space.  Bull. Lond. Math. Soc. 57 (2025), no. 8, 2477–2488.

22. The horospherical $p$-Christoffel-Minkowski problem in hyperbolic space (with Tianci Luo),   Nonlinear Anal., Volume 257, August 2025, 113799

21. Volume preserving nonhomogeneous Gauss curvature flow in hyperbolic space (with Bo Yang and Tailong Zhou), Pure Appl. Math. Q., Volume 21, Number 4, 1607–1643, 2025

20. A Heintze-Karcher type inequality for capillary hypersurfaces in hyperbolic half-space (with Yingxiang Hu, Chao Xia and Tailong Zhou),  J. Funct. Anal. 289, no. 6, 110970, 2025.

19. A complete family of Alexandrov-Fenchel inequalities for convex capillary hypersurfaces in the half-space (with Yingxiang Hu, Bo Yang and Tailong Zhou),  Math. Ann., 390 (2024), no. 2, 3039–3075.

18. Volume preserving Gauss curvature flow of convex hypersurfaces in H^{n+1} (with Bo Yang and Tailong Zhou),   Trans. Amer. Math. Soc. 377 (2024), no. 4, 2821–2854.

17. Evolution of graphs in hyperbolic space by their Gauss curvature (with Shujing Pan).  Nonlinear Anal. 241 (2024), Paper No. 113477, 17 pp. 

16. On the mean curvature type flow for convex capillary hypersurfaces in the ball (with Yingxiang Hu, Bo Yang, Tailong Zhou),  Calc.Var.Partial Differ. Equ., Vol. 62, no. 7, article no. 209, 2023.

15. Geometric inequalities involving three quantities in warped product manifolds (with Kwok-Kun Kwong), Advances in Math. ,Vol. 430, 1 Oct 2023, article no. 109213.

14. Shifted inverse curvature flows in hyperbolic space (with Xianfeng Wang and Tailong Zhou), Calc.Var.Partial Differ. Equ., 62 (2023), no.3, article no.93.

13. Volume preserving flows for convex curves and surfaces in the hyperbolic space (with Bo Yang), J. Func. Anal., 283, no. 11, Article 109685, 2022.

12. On an inverse curvature flow in two-dimensional space forms (with Kwok-Kun Kwong, Glen Wheeler, and Valentina-Mira Wheeler), Math. Ann. (2022) 384: 285-308.

11. Locally constrained curvature flows and geometric inequalities in hyperbolic space (with Yingxiang Hu and Haizhong Li), Math. Ann., (2022) 382:1425-1474. 

10. A volume-preserving anisotropic mean curvature type flow (with Changwei Xiong), Indiana Univ. Math. J.70 (2021), 881-906. 

9. Volume preserving flow and Alexandrov-Fenchel type inequalities in hyperbolic space (with Ben Andrews and Xuzhong Chen), J. Eur. Math. Soc., 23 (2021), no. 7, 2467-2509. 

8. Volume preserving flow by powers of kth mean curvature (with Ben Andrews), J. Differential Geom, 117 (2021), no. 2 , 193-222. 

7. Stability of torsion-free G2 structure along the Laplacian flow (with Jason D. Lotay), J. Differential Geom., 111 (2019), no. 3, 495-526.

6. Quermassintegral preserving curvature flow in hyperbolic space (with Ben Andrews), Geom. Funct. Anal., 2018, 28(5), 1183-1208.

5. On the Minkowski-type inequality for outward minimizing hypersurfaces in Schwarzschild space, Calc.Var.Partial Differ. Equ., 2018, vol. 57, no. 2, article no. 46.

4. On inverse mean curvature flow in Schwarzchild space and Kottler space (with Haizhong Li), Calc.Var.Partial Differ. Equ.,2017, vol. 56, no. 3, article no. 62

3. Laplacian flow for closed G2 structures: Shi-type estimate, uniqueness and compactness (with Jason D. Lotay), Geom. Funct. Anal., 2017, 27(1), 165-233.

2. Smooth compactness of f-minimal hypersurfaces with bounded f-index (with Ezequiel Barbosa and Ben Sharp),  Proc. Amer. Math. Soc. 145 (2017), no. 11, 4945–4961.

1. A geometric inequality on hypersurface in hyperbolic space (with Haizhong Li and Changwei Xiong), Advances in Math., 2014, 253(1):152-162