Papers and Preprints:

  1. (With X. Wang) Generalized Alexandrov theorems in spacetimes with integral conditions. arXiv preprint.
  2. (With Y. Wei) Geometric inequalities involving three quantities in warped product manifolds. Adv. Math. Vol. 430, 1 October 2023, 109213. arXiv preprint.
  3. Effect of the average scalar curvature on Riemannian manifolds. arXiv preprint.
  4. (With J. Chu, M-C. Lee) Rigidity on non-negative intermediate curvature. To appear in Math. Res. Lett. arXiv preprint.
  5. An estimate for the genus of embedded surfaces in the 3-sphere. To appear in J. Geom. Anal. arXiv preprint.
  6. (With H. Lee) Length-minimizing level curves via calibrations. arXiv preprint.
  7. A unified approach to higher order discrete and smooth isoperimetric inequalities. Mathematika Vol. 70, Issue 1, Jan 2024. arXiv preprint.
  8. Higher order Poincare inequalities and Minkowski-type inequalities. arXiv preprint.
  9. (With Y. Wei, G. Wheeler, V-M. Wheeler) On an inverse curvature flow in two-dimensional space forms. Math. Ann. 384: 1–24, 2022. arXiv preprint.
  10. (With H. Lee) Higher order Wirtinger-type inequalities and sharp bounds for the isoperimetric deficit. Proc. Amer. Math. Soc. 149(11), 4825-4840, 2021. arXiv preprint.
  11. (With T. L. J. Ng) Universal approximation on the hypersphere. Comm. in Statistics - Theory & Methods Vol. 51, Issue 24, 2022. arXiv preprint.
  12. Some sharp isoperimetric-type inequalities on Riemannian manifolds. J. Geom. Phys. 181, Nov 2022, 104647. arXiv preprint.
  13. Quantitative comparison theorems in Riemannian and Kähler geometry. arXiv preprint.
  14. Weighted isoperimetric inequalities in warped product manifolds. Differ. Geom. Appl. Vol. 89, Aug 2023, 102011. arXiv preprint.
  15. (With H. Lee, J. Pyo) Weighted Hsiung-Minkowski formulas and rigidity of umbilical hypersurfaces. Math. Res. Lett. 25 (2): 597-616, 2018. arXiv preprint.
  16. (With P. Miao) A functional inequality on the boundary of static manifolds. Asian J. Math. 21 (4): 687-696, 2017. arXiv preprint.
  17. Some sharp Hodge Laplacian and Steklov eigenvalue estimates for differential forms. Cal. Var. and PDE. 55 (2): 1-14, 2016. arXiv preprint.
  18. An extension of Hsiung-Minkowski formulas and some applications. J. Geom. Anal. 26 (1): 1-23, 2016. arXiv preprint.
  19. (With P. Miao) Monotone quantities involving a weighted σk integral along inverse curvature flows. Comm. Contemp. Math. 17 (5), 2015. arXiv preprint.
  20. On an inequality of Andrews, De Lellis, and Topping. J. Geom. Anal. 25 (1): 108-121, 2015. arXiv preprint.
  21. (With P. Miao) A new monotone quantity along the inverse mean curvature flow in Rn. Pac. J. Math. 267 (2): 417-422, 2014. arXiv preprint.
  22. (With X-Q. Fan) A property of the Brown-York mass in Schwarzschild manifolds. J. Math. Anal. and Appl. 400 (2): 615-623, 2013. arXiv preprint.
  23. On the positivity of a quasi-local mass in general dimensions. Comm. Anal. Geom. 21 (4): 847-871, 2013. arXiv preprint.
  24. (With L-F. Tam) Limit of quasilocal mass integrals in asymptotically hyperbolic manifolds. Proc. Amer. Math. Soc. 141: 313-324, 2013. arXiv preprint.
  25. (With X-Q. Fan) The Brown-York mass of revolution surfaces in asymptotically Schwarzschild Manifolds. J. Geom. Anal. 21 (3): 527-542, 2011. arXiv preprint.

Theses:

  • Floer homology on symplectic manifolds. M.Phil. thesis. Available here.
  • On the limiting behaviors and positivity of quasi-local mass. Ph.D. thesis. Available here.

Other: