Research

Research interests: Differential Geometry, Geometric Analysis. In particular: Ricci flow, singularity analysis, classification and geometry of Ricci soliton, gap theorem for Riemannian manifolds, scalar curvature and the mathematical theory of general relativity.

List of publications/accepted papers:

1. (with Z. Ma and Y. Zhang) Dimension Reduction for Positively Curved Steady Solitons, Ann Glob Anal Geom 67, 20 (2025). https://doi.org/10.1007/s10455-025-10001-8

2. (with Z. Ma and Y. Zhang) Ancient Ricci flows with asymptotic solitons, J Geom Anal 35, 199 (2025). https://doi.org/10.1007/s12220-025-02034-z

3. (with S. Huang and M.-C. Lee) Manifolds with small curvature concentration,  Ann. PDE 10, 23 (2024). https://doi.org/10.1007/s40818-024-00183-y

4. (with M.-C. Lee) Gap Theorem on manifolds with small curvature concentration, Math. Z. 308, 9 (2024). https://doi.org/10.1007/s00209-024-03570-0

5. (with Z. Ma and Y. Zhang) On Ricci flows with closed and smooth tangent flows, Calc. Var. Partial Differential Equations 63 (2024), no. 7, Paper No. 179, 31 pp. https://doi.org/10.1007/s00526-024-02778-6

6. (with Z. Ma and Y. Zhang) Local smooth convergence of F-limit flows, International Journal of Mathematics. https://doi.org/10.1142/S0129167X24500472

7. (with J. Chu, M.-C. Lee and T.-Y. Tsang) Monotonicity of the p-Green functions, International Mathematics Research Notices, Volume 2024, Issue 9, May 2024, Pages 7998–8025, https://doi.org/10.1093/imrn/rnae030 

8. (with Z. Ma and Y. Zhang) A local Sobolev inequality on Ricci flow and its applications, J. Funct. Anal. 285 (2023), no. 5, Paper No. 109995, 36 pp. https://doi.org/10.1016/j.jfa.2023.109995

9. (with R. Bamler, Z. Ma and Y. Zhang) An optimal volume growth estimate for noncollapsed steady gradient Ricci solitons, Peking Math J 6, 353–364 (2023). https://doi.org/10.1007/s42543-023-00060-w

10. (With B. Chow, Z. Ma and Y. Zhang) Lower bounds for the scalar curvatures of Ricci flow singularity models, J. Reine Angew. Math.794 (2023), 253–265. https://doi.org/10.1515/crelle-2022-0086

11. (with Z. Ma and Y. Zhang) The rate of F-convergence for Ricci flows with closed and smooth tangent flows, J Geom Anal 32, 293 (2022). https://doi.org/10.1007/s12220-022-01023-w

12. (with Z. Ma and Y. Zhang) Volume growth estimates of gradient Ricci solitons, J Geom Anal 32, 291 (2022). https://doi.org/10.1007/s12220-022-01026-7

13. (with Z. Ma and Y. Zhang) A uniform Sobolev inequality for ancient Ricci flows with bounded Nash entropy, International Mathematics Research Notices, rnac146, https://doi.org/10.1093/imrn/rnac146

14. (with B. Zhu) On a dichotomy of the curvature decay of steady Ricci solitons, Advances in Mathematics, Volume 404, 2022, Paper No. 108458, 40 pp. https://doi.org/10.1016/j.aim.2022.108458

15. (with E. Chen and M.-C. Lee) Small curvature concentration and Ricci flow smoothing. J. Funct.  Anal. 282 (2022), no. 10, Paper No. 109420, 29 pp. https://doi.org/10.1016/j.jfa.2022.109420

16. Curvature estimates and gap theorems for expanding Ricci solitons, International Mathematics Research Notices, rnab257, https://doi.org/10.1093/imrn/rnab257

17.  Gradient steady Kahler Ricci solitons with non-negative Ricci curvature and integrable scalar curvature, Comm. Anal. Geom. 30 (2022), no. 2, 271 – 296. https://dx.doi.org/10.4310/CAG.2022.v30.n2.a2

18. Curvature estimates for steady Ricci solitons, Trans. Amer. Math. Soc. 372 (2019), no. 12, 8985– 9008. https://doi.org/10.1090/tran/7954

19. (with L. F. Tam) A note on center of mass, Comm. Anal. Geom. 24, 471 – 486 (2016). https://dx.doi.org/10.4310/CAG.2016.v24.n3.a2

Preprints:

1. (with M.-C. Lee) On the weakly conical expanding gradient Ricci solitons, arXiv:2503.12416 (2025).

2. (with M.-C. Lee and L. T. Peachey) Expanding Ricci solitons coming out of weakly PIC1 metric cones, arXiv:2404.12755v2 (2024).

3. (with R. J. Conlon and Y. Lai) A family of Kähler flying wing steady Ricci solitons, arXiv:2403.04089v2 (2024).

4. (with Z. Ma and Y. Zhang) On noncollapsed F-limit metric solitons, arXiv:2401.03387 (2024).

5. (with M.-C. Lee) Gap Theorem on Riemannian manifolds using Ricci flow, arXiv:2305.01396 (2023).

6. (with Z. Ma and Y. Zhang) A local gap theorem for Ricci shrinkers, arXiv:2212.09203 (2022).

7. (with Z. Ma and Y. Zhang) Hamilton-Ivey estimates for gradient Ricci solitons, arXiv:2112.11025 (2021).