Research
31. CW complex hypothesis for image data. (With Zhiren Wang)
Accepted by International Conference on Machine Learning (ICML) (2024)
30. Fully nonlinear Yamabe type problems on noncompact manifolds. arxiv (With Jonah Duncan)
29. Fast equilibrium of SGD in generic situations. Accepted by The International Conference on Learning Representations (ICLR) 2024. (With Zhiyuan Li, Zhiren Wang)
28. Stability of quermassintegral inequalities along inverse curvature flows. arxiv, accepted by Calc. Var. Partial Differential Equations (2024). (With Caroline VanBlargan)
27. The Yamabe flow on asymptotically flat manifolds. arxiv
Accepted by J. Reine Angew. Math. (Crelle's journal) (2023). (With Eric Chen)
26. The Neumann problem on the domain in S^3 bounded by the Clifford torus. Dedicated to David Jerison on the occasion of his 70th birthday. arxiv Accepted by Advanced Nonlinear Studies (2023). (With Jeffrey S. Case, Eric Chen, Paul Yang, and Po-Lam Yung)
25. Quantitative quermassintegral inequalities for nearly spherical sets. arxiv
Accepted by Commun. Contemp. Math. (2023). (With Caroline VanBlargan)
24. The Yamabe flow on asymptotically Euclidean manifolds with nonpositive
Yamabe constant. arxiv Accepted by J. Funct. Anal. (2022). (With Gilles Carron, Eric Chen)
23. Three-stage evolution and fast equilibrium for SGD with non-degenerate critical points. International Conference on Machine Learning (ICML) (2022). paper (With Zhiren Wang)
22. The Dirichlet principle for the complex k-Hessian functional. arxiv
Accepted by Comm. Anal. Geom. (2021). (With Hang Xu)
21. Sun-Yung Alice Chang and geometric analysis. paper
Notices of the AMS., March (2020). (With Matthew Gursky)
20. Towards a fully nonlinear sharp Sobolev trace inequality. arxiv
Journal of Mathematical Study, 53 (2020), pp. 402-435. (With Jeffrey Case)
19. On the Sobolev-Poincare inequality of CR-manifolds. arxiv
Int. Math. Res. Not. IMRN. (2020) no. 18, 5661-5678. (With Paul Yang)
18. Nonuniqueness for a fully nonlinear boundary Yamabe-type problem via bifurcation theory. arxiv
Calc. Var. Partial Differential Equations, (2019) 58:106. (With Jeffrey Case and Ana Claudia Moreira)
17. Approximation in fractional Sobolev spaces and Hodge systems. arxiv
J. Funct. Anal. 276 (2019), no. 5, 1430-1478. (With Pierre Bousquet, Emmanuel Russ, Po-Lam Yung)
16. Boundary operators associated to the σk-curvature. arxiv
Adv. Math., Vol. 337 (2018), 83-106. (With Jeffrey Case)
15. Integrability of scalar curvature and normal metric on conformally flat manifolds. arxiv
J. Differential Equations 265 (2018), no. 4, 1353-1370. (With Shengwen Wang)
14. Fractional Poincare inequalities in various settings. paper
Bruno Pini Mathematical Analysis Seminar (2017), 43-54. (With Yannick Sire)
13. Isoperimetric inequality on CR malifolds with nonnegative Q-curvature. arxiv
Annali della Scuola Normale Superiore di Pisa (5) 18 (2018), no. 1, 343-362. (With Paul Yang)
12. A Dirichlet's principle for the k-Hessian. arxiv
J. Funct. Anal. 275 (2018), no. 11, 2895-2916. (With Jeffrey Case)
11. Fractional Poincare inequality with finite total Q-curvature. arxiv
Calc. Var. Partial Differential Equations 56 (2017), no. 2, Art. 35, 18 pp. (With Yannick Sire)
10. Isoperimetric inequality, Q-curvature and Ap weights. arxiv
Adv. Math., Vol. 281 (2016), 823-844.
9. On locally conformally flat manifolds with finite total Q-curvature. arxiv
Calc. Var. Partial Differential Equations (2017), no. 4, Art. 98, 24 pp. (With Zhiqin Lu)
8. Finite total Q-curvature in conformal geometry and the CR geometry. paper
Oberwolfach Report-Partial Differential Equations, Vol. 36, (2015).
7. A subelliptic Bourgain-Brezis inequality. arxiv
J. Eur. Math. Soc. (JEMS), Vol. 16, Issue 4, (2014), 649-693. (With Po-Lam Yung)
6. Some higher order isoperimetric inequalities via the method of optimal transport. arxiv
Int. Math. Res. Not. IMRN (2014) no. 24, 6619-6644. (With Sun-Yung Alice Chang)
5. Michael-Simon inequalities for k-th mean curvatures. arxiv
Calc. Var. Partial Differential Equations (2014), Vol. 51, no. 1, 117-138.
4. Inequalities for quermassintegrals on k-convex domains. paper
Adv. Math., Vol. 248 (2013), 335-377. (With Sun-Yung Alice Chang)
3. The isoperimetric inequality and quasiconformal maps on manifolds with finite total Q-curvature. arxiv Int. Math. Res. Not. IMRN (2012) no. 2, 394-422.
2. On Aleksandrov-Fenchel inequalities for k-convex domains. paper
Milan J. Math., Vol. 79 (2011), 13-38. (With Sun-Yung Alice Chang)
1. On some geometric inequalities and applications, 2011, Princeton University. (Ph.D Thesis)
Locating the blow-up points of higher order Liouville equations, 2006, Chinese University of Hong Kong. (Master Thesis)