I am interested in elliptic and parabolic partial differential equations and their applications in geoemtric analysis and optimal transportation.
- Continuity for the Monge mass transfer problem in two dimensions (joint with F. Santambrogio and X.-J. Wang). Submitted in 2016.
- Flow by Gauss curvature to the Aleksandrov and dual Minkowski problems (joint with W. Sheng and X.-J. Wang). Accepted by J. Eur. Math. Soc. (JEMS) in 2017.
- Infinitely many solutions for centro-affine Minkowski problem. Submitted in 2016.
- Two dimensional Monge-Ampère equations under incomplete Hölder assumptions. Accepted by Math. Res. Lett. in 2016.
- On the Lp Monge-Ampère equation (joint with S. Chen and G. Zhu). To appear in J. Differential Equations. https://doi.org/10.1016/j.jde.2017.06.007
- Multiple solutions of the Lp-Minkowski problem (joint with Y. He and X.-J. Wang). Calc. Var. Partial Differential Equations 55 (2016), no. 5, Paper No. 117, 13 pp.
- Regularity of the homogeneous Monge-Ampère equation (joint with X.J. Wang). Discrete Contin. Dyn. Syst. 35 (2015), no. 12, 6069--6084.
- Regularity in Monge's mass transfer problem (joint with F. Santambrogio and X.-J. Wang). J. Math. Pures Appl. (9) 102 (2014), no. 6, 1015--1040.
- Positivity of Ma-Trudinger-Wang curvature on Riemannian surfaces (joint with S.-Z. Du). Calc. Var. Partial Differential Equations 51 (2014), no. 3-4, 495--523.
- Closed hypersurfaces with prescribed Weingarten curvature in Riemannian manifolds (joint with W. Sheng). Calc. Var. Partial Differential Equations 48 (2013), no. 1-2, 41--66.
- Some Dirichlet problems arising from conformal geometry (joint with W. Sheng). Pacific J. Math. 251 (2011), no. 2, 337--359.
- Surfaces expanding by the power of the Gauss curvature flow. Proc. Amer. Math. Soc. 138 (2010), no. 11, 4089--4102.