Papers and Preprints:
- (With X. Wang) Generalized Alexandrov theorems in spacetimes with integral conditions. arXiv preprint.
- (With Y. Wei) Geometric inequalities involving three quantities in warped product manifolds. Adv. Math. Vol. 430, 1 October 2023, 109213. arXiv preprint.
- Effect of the average scalar curvature on Riemannian manifolds. arXiv preprint.
- (With J. Chu, M-C. Lee) Rigidity on non-negative intermediate curvature. To appear in Math. Res. Lett. arXiv preprint.
- An estimate for the genus of embedded surfaces in the 3-sphere. To appear in J. Geom. Anal. arXiv preprint.
- (With H. Lee) Length-minimizing level curves via calibrations. arXiv preprint.
- A unified approach to higher order discrete and smooth isoperimetric inequalities. Mathematika Vol. 70, Issue 1, Jan 2024. arXiv preprint.
- Higher order Poincare inequalities and Minkowski-type inequalities. arXiv preprint.
- (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.
- (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.
- (With T. L. J. Ng) Universal approximation on the hypersphere. Comm. in Statistics - Theory & Methods Vol. 51, Issue 24, 2022. arXiv preprint.
- Some sharp isoperimetric-type inequalities on Riemannian manifolds. J. Geom. Phys. 181, Nov 2022, 104647. arXiv preprint.
- Quantitative comparison theorems in Riemannian and Kähler geometry. arXiv preprint.
- Weighted isoperimetric inequalities in warped product manifolds. Differ. Geom. Appl. Vol. 89, Aug 2023, 102011. arXiv preprint.
- (With H. Lee, J. Pyo) Weighted Hsiung-Minkowski formulas and rigidity of umbilical hypersurfaces. Math. Res. Lett. 25 (2): 597-616, 2018. arXiv preprint.
- (With P. Miao) A functional inequality on the boundary of static manifolds. Asian J. Math. 21 (4): 687-696, 2017. arXiv preprint.
- Some sharp Hodge Laplacian and Steklov eigenvalue estimates for differential forms. Cal. Var. and PDE. 55 (2): 1-14, 2016. arXiv preprint.
- An extension of Hsiung-Minkowski formulas and some applications. J. Geom. Anal. 26 (1): 1-23, 2016. arXiv preprint.
- (With P. Miao) Monotone quantities involving a weighted σk integral along inverse curvature flows. Comm. Contemp. Math. 17 (5), 2015. arXiv preprint.
- On an inequality of Andrews, De Lellis, and Topping. J. Geom. Anal. 25 (1): 108-121, 2015. arXiv preprint.
- (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.
- (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.
- On the positivity of a quasi-local mass in general dimensions. Comm. Anal. Geom. 21 (4): 847-871, 2013. arXiv preprint.
- (With L-F. Tam) Limit of quasilocal mass integrals in asymptotically hyperbolic manifolds. Proc. Amer. Math. Soc. 141: 313-324, 2013. arXiv preprint.
- (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: