Qi-Rui Li

Ph.D.
Postdoctoral Fellow

Read more about Qi-Rui's biography and research interests.

Research interests

I am interested in elliptic and parabolic partial differential equations and their applications in geoemtric analysis and optimal transportation.

Groups

  • Continuity for the Monge mass transfer problem in two dimensions (with F. Santambrogio and X.-J. Wang). Submitted in 2016.
  • On the planar Dual Minkowski problem (with S. Chen). Submitted in 2017.
  • Asymptotic convergence for a class of fully nonlinear curvature flows (with W. Sheng and X.-J. Wang). Submitted in 2017.
  • Flow by Gauss curvature to the Aleksandrov and dual Minkowski problems (with W. Sheng and X.-J. Wang). Accepted by J. Eur. Math. Soc. (JEMS) in 2017.
  • Infinitely many solutions for centro-affine Minkowski problem. Accepted by Int. Math. Res. Not. (IMRN) in 2017.
  • The logarithmic Minkowski problem for non-symmetric measures (with S. Chen and G. Zhu). Accepted by Trans. Amer. Math. Soc. in 2017. DOI: https://doi.org/10.1090/tran/7499.
  • A class of optimal transportation problem on the sphere, Dedicated to Professor G.C. Dong on the occasion of his 90th birthday (with X.-J. Wang). Sci Sin Math. 48 (2018), no. 1, 181--200.
  • On the Lp Monge-Ampère equation (with S. Chen and G. Zhu).  J. Differential Equations 263 (2017), no. 8, 4997--5011.
  • Two dimensional Monge-Ampère equations under incomplete Hölder assumptions. Math. Res. Lett. 24 (2017), no. 2, 481--502.
  • Multiple solutions of the Lp-Minkowski problem (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 (with X.J. Wang). Discrete Contin. Dyn. Syst. 35 (2015), no. 12, 6069--6084. 
  • Regularity in Monge's mass transfer problem (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 (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 (with W. Sheng). Calc. Var. Partial Differential Equations 48 (2013), no. 1-2, 41--66. 
  • Some Dirichlet problems arising from conformal geometry (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.